01234_01243_01324_02134_02143_02314_03124_03214_12034_12043_12304_13024_13204_23014_23104
Counting sequence:
1, 1, 2, 6, 24, 105, 480, 2264, 10940, 53891, 269650, 1366754, 7002992, 36214028, 188760920, 990695008, 5231104228, 27769535703, 148119330278, 793429253082, 4266533814888, 23022665992569, 124627400178352, 676597733475240, 3683009458071312, 20097357249860116, 109915229103874712, 602403482891473848, 3307983305322361696, 18198161901952513112, 100283158743187285256, 553500014634929370304, 3059522748912787012916, 16935470893442547907519, 93866998950902102737518, 520916603804587223242202, 2894231785761072527334312, 16098332217672928234955019, 89636668029396277124651040, 499602344321058207774766376, 2787248000891886820621192700, 15563925591292509587871357947, 86983422731660560146614779474, 486530832369838352058378930578, 2723482918635007114275512725520, 15256830159474408625241311021600, 85529368441872546267851270022432, 479804525186118800533036662887424, 2693389592069362053650070372364016, 15128928635532528668500369382952228, 85031613071276334198598453630620584, 478195665283091457160708953569563672, 2690754916819968446121494096751036768, 15148750140930793641559299659705578572, 85330635979255214314158215000857846848, 480895284642118103243897882327974976352, 2711475487837224088183008852048652070880, 15295481432999634270019855199149131597240, 86320903604507108716213079207771873778192, 487368625941016539827359304863822775834256, 2752844349245656275915057206095253733318432, 15555439376236573381328707734189777751380384, 87933381673835284403531231740846593704663784, 497268250247613090289694989982918531987607936, 2813118323708783031372493464908849948831624148, 15919912143269473037027736646696494601202217615, 90124743360722500432972374851772788463861019902, 510379991730738997739101230486705900199294039322, 2891246899821005154437644480918405284578637393384, 16383797075006752562826087215925376051526224385679, 92870515604655576938193294264665737144242615027104, 526588426954274874934136529898721502677157743235240, 2986698045614749037963605235226339283043413713937652, 16944721056292841669695341107121595344433935824605801, 96160632819969027978486913987750129349089440145911638, 545854381334696594546913133600685267542497216254264358, 3099344337032494061230319590617580219734047779414164624, 17602463744551399384393509767334289322901703879096265820, 99996514410205826191768492882451781753215970067670724696, 568200118149278815773757060964568380640701810605661854688, 3229387896889284530217311832840187274466554249088285174788, 18358577248647387008600261824654435018882700076492477765887, 104389138627508688930412694598041920969630798869251264463190, 593699590653885803201505729614548255885991352465489361023242, 3377311113306346726096283635530379774829626186239943276546472, 19216137324443782491849225106140697741223780589127067476781881, 109357788698396727437993563082215728219217979570963300566787888, 622472137393036444527477277084302185699498582990071468159345768, 3543845028633541528036119184009565808734524208513709481183638144, 20179585438903699473464831079460108101959729269794161145518122448, 114929267189905026099611358937007734624246340313394281898001419104, 654678595358367327663125510078737080244427628086506726253543462880, 3729950239917717745313158938424939043809385263671230012479542059136, 21254635717537868211479378793394672105458328586557711278654207886688, 121137447598014961541297550951970790029554569829942987913113814738656, 690519169784321398944534563722206902556265773269016927455503485572864, 3936806971158123841877564716253445894814145750633639714230293616003888, 22448229893512591164003728781893747593365470042354414875887713745218628, 128023077769889605427098558528003641358174799417501494706117079743672648, 730232628445961308647037144226797317192687430638436266394687069966271768, 4165812129453410121608311790101857239853424465071949861092492920991401312
Implicit equation for the generating function in Maple syntax:
x^2*(x-2)*F(x)^3+x*(x^2-2*x+8)*F(x)^2+(-3*x^3-9*x-2)*F(x)+x^3+x^2+3*x+2 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x -2\right) F \! \left(x \right)^{3}+x \left(x^{2}-2 x +8\right) F \! \left(x \right)^{2}+\left(-3 x^{3}-9 x -2\right) F \! \left(x \right)+x^{3}+x^{2}+3 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 105
a(6) = 480
a(7) = 2264
a(8) = 10940
a(n+9) = 1/2*n*(n+1)/(n+10)/(n+9)*a(n)-1/8*(28*n+57)*(n+1)/(n+10)/(n+9)*a(n+1)+1/64*(213*n^2+48*n-989)/(n+10)/(n+9)*a(n+2)-1/384*(1451*n^2+3233*n-2478)/(n+10)/(n+9)*a(n+3)+1/192*(1304*n^2+2057*n-23145)/(n+10)/(n+9)*a(n+4)+1/96*(2365*n^2+25891*n+71898)/(n+10)/(n+9)*a(n+5)-1/16*(251*n^2+2478*n+5163)/(n+10)/(n+9)*a(n+6)-1/24*(272*n^2+4661*n+19851)/(n+10)/(n+9)*a(n+7)+1/12*(97*n+829)/(n+10)*a(n+8), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 24
a \! \left(5\right) = 105
a \! \left(6\right) = 480
a \! \left(7\right) = 2264
a \! \left(8\right) = 10940
a \! \left(n +9\right) = \frac{n \left(n +1\right) a \! \left(n \right)}{2 \left(n +10\right) \left(n +9\right)}-\frac{\left(28 n +57\right) \left(n +1\right) a \! \left(n +1\right)}{8 \left(n +10\right) \left(n +9\right)}+\frac{\left(213 n^{2}+48 n -989\right) a \! \left(n +2\right)}{64 \left(n +10\right) \left(n +9\right)}-\frac{\left(1451 n^{2}+3233 n -2478\right) a \! \left(n +3\right)}{384 \left(n +10\right) \left(n +9\right)}+\frac{\left(1304 n^{2}+2057 n -23145\right) a \! \left(n +4\right)}{192 \left(n +10\right) \left(n +9\right)}+\frac{\left(2365 n^{2}+25891 n +71898\right) a \! \left(n +5\right)}{96 \left(n +10\right) \left(n +9\right)}-\frac{\left(251 n^{2}+2478 n +5163\right) a \! \left(n +6\right)}{16 \left(n +10\right) \left(n +9\right)}-\frac{\left(272 n^{2}+4661 n +19851\right) a \! \left(n +7\right)}{24 \left(n +10\right) \left(n +9\right)}+\frac{\left(97 n +829\right) a \! \left(n +8\right)}{12 n +120}, \quad n \geq 9
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24287/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[14,x,k[0]]+F[16,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]*F[7,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[9,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]*F[9,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_14(x, k_0) + F_16(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x)*F_7(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_9(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_10(x, k_0)*F_13(x, k_0)*F_9(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_10(x, k_0)*F_13(x, k_0)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, 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[2, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 1], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24288/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[17,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]]*F[3,x]*F[7,x,k[1]]
F[14,x,k[0]] = F[1,x]+F[9,x,k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[10,x,k[1]]*F[14,x,k[0]]*F[9,x,k[1]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[11,x,k[1],k[0]]*F[14,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , z , y\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right) F_{7}\! \left(x , z\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = F_{10}\! \left(x , z\right) F_{14}\! \left(x , y\right) F_{9}\! \left(x , z\right)
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{11}\! \left(x , z , y\right) F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_15(x, k_0, k_1) + F_17(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0)*F_3(x)*F_7(x, k_1))
Eq(F_14(x, k_0), F_1(x) + F_9(x, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_10(x, k_1)*F_14(x, k_0)*F_9(x, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_11(x, k_1, k_0)*F_14(x, k_0)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 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"pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": 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