English

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}
}
R2 v1 2026-06-22T12:41:20.904Z