Rationality for subclasses of 321-avoiding permutations
Combinatorics
2019-01-03 v3
Abstract
We prove that every proper subclass of the 321-avoiding permutations that is defined either by only finitely many additional restrictions or is well quasi-ordered has a rational generating function. To do so we show that any such class is in bijective correspondence with a regular language. The proof makes significant use of formal languages and of a host of encodings, including a new mapping called the panel encoding that maps languages over the infinite alphabet of positive integers avoiding certain subwords to languages over finite alphabets.
Keywords
Cite
@article{arxiv.1602.00672,
title = {Rationality for subclasses of 321-avoiding permutations},
author = {Michael H. Albert and Robert Brignall and Nik Ruškuc and Vincent Vatter},
journal= {arXiv preprint arXiv:1602.00672},
year = {2019}
}