The Permutation Pattern Avoidance Library (PermPAL)

PermPAL is a database of algorithmically-derived theorems about permutation classes.

The Combinatorial Exploration framework produces rigorously verified combinatorial specifications for families of combinatorial objects. These specifications then lead to generating functions, counting sequence, polynomial-time counting algorithms, random sampling procedures, and more.

This database contains 23,845 permutation classes for which specifications have been automatically found. This includes many classes that have been previously enumerated by other means and many classes that have not been previously enumerated.

Some Notables Successes:

Section 2.4 of the article Combinatorial Exploration: An Algorithmic Framework for Enumeration gives a more comprehensive list of notable results.

The comb_spec_searcher github repository contains the open-source python framework for Combinatorial Exploration, and the tilings github repository contains the code needed to apply it to the field of permutation patterns.

If PermPAL has been a useful tool for your research, please consider citing it:
@misc{combinatorial-exploration,
    title={Combinatorial {E}xploration: An algorithmic framework for enumeration},
    author={Michael H. Albert and Christian Bean and Anders Claesson and \'Emile Nadeau and Jay Pantone and Henning Ulfarsson},
    year={2022},
    eprint={2202.07715},
    archivePrefix={arXiv},
    primaryClass={math.CO},
    howpublished={\url{https://arxiv.org/abs/2202.07715}},
}