Uncountably many enumerations of well-quasi-ordered permutation classes
Combinatorics
2026-04-23 v4
Abstract
We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in fact shows that many such classes lack D-finite or D-algebraic generating functions. Our construction is based on an uncountably large collection of factor-closed, well-quasi-ordered binary languages due to Pouzet.
Keywords
Cite
@article{arxiv.2211.12397,
title = {Uncountably many enumerations of well-quasi-ordered permutation classes},
author = {Robert Brignall and Vincent Vatter},
journal= {arXiv preprint arXiv:2211.12397},
year = {2026}
}