Rationality for subclasses of 321-avoiding permutations
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.
Citation
Albert , M H , Brignall , R , Ruskuc , N & Vatter , V 2019 , ' Rationality for subclasses of 321-avoiding permutations ' , European Journal of Combinatorics , vol. 78 , pp. 44-72 . https://doi.org/10.1016/j.ejc.2019.01.001
Publication
European Journal of Combinatorics
Status
Peer reviewed
ISSN
0195-6698Type
Journal article
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.