Combinatorial specification of permutation classes
Combinatorics
2012-04-05 v1
Abstract
This article presents a methodology that automatically derives a combinatorial specification for the permutation class C = Av(B), given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is achieved considering both pattern avoidance and pattern containment constraints in permutations.The obtained specification yields a system of equations satisfied by the generating function of C, this system being always positiveand algebraic. It also yields a uniform random sampler of permutations in C. The method presentedis fully algorithmic.
Keywords
Cite
@article{arxiv.1204.0797,
title = {Combinatorial specification of permutation classes},
author = {Frédérique Bassino and Mathilde Bouvel and Adeline Pierrot and Carine Pivoteau and Dominique Rossin},
journal= {arXiv preprint arXiv:1204.0797},
year = {2012}
}