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THE PERMUTATION PATTERN AVOIDANCE LIBRARY (PERMPAL)

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

The TODO TODO TODOCombinatorial 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 15089 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:

 * 4 out of 7 of the principal classes of length 4
 * all 56 symmetry classes avoiding two patterns of length 4
 * all 317 symmetry classes avoiding three patterns of length 4
 * the "domino set" used by Bevan, Brignall, Elvey Price, and Pantone to
   investigate Av(1324)
 * the class Av(3412, 52341, 635241) of Alland and Richmond corresponding a type
   of Schubert variety
 * the class Av(2341, 3421, 4231, 52143) equal to the (Av(12), Av(21))-staircase
   (see Albert, Pantone, and Vatter), which appears to be non-D-finite
 * all of the permutation classes counted by the Schröder numbers conjectured by
   Eric Egge
 * the class Av(34251, 35241, 45231), equal to the preimage of Av(321) under the
   West-stack-sorting operation (see Defant)

Section 2.4 of the article TODO TODO TODOCombinatorial 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:
copy to clipboard

@unpublished{combinatorial-exploration,
    author = {Albert, Michael H. and Bean, Christian and Claesson, Anders and Nadeau, \'{E}mile and Pantone, Jay and Ulfarsson, Henning},
    note = {(forthcoming)},
    title = {Combinatorial {E}xploration: An Algorithmic Framework for Enumeration},
}

Questions, comments, bug reports, and feature suggestions are very welcome!
Contact jay.pantone@marquette.edu.
If this database has been useful to your research, please consider citing it.