An algorithm computing combinatorial specifications of permutation classes

Frédérique Bassino (1) , Mathilde Bouvel (2) , Adeline Pierrot (3, 4) , Carine Pivoteau (5) , Dominique Rossin (6)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 BioInfo - LRI - Bioinformatique (LRI)
5 LIGM - Laboratoire d'Informatique Gaspard-Monge
6 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, 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 positive and algebraic. It also yields a uniform random sampler of permutations in C. The method presented is fully algorithmic.

Domains: Combinatorics [math.CO]

Frédérique Bassino, Mathilde Bouvel, Adeline Pierrot, Carine Pivoteau, Dominique Rossin. An algorithm computing combinatorial specifications of permutation classes. Discrete Applied Mathematics, 2017, 224, pp.16-44. ⟨10.1016/j.dam.2017.02.013⟩. ⟨hal-01175234⟩