Authors: Frédérique Bassino ¹; Mathilde Bouvel ²; Adeline Pierrot ³; Carine Pivoteau ⁴; Dominique Rossin ⁵

• 1 Laboratoire d'Informatique de Paris-Nord
• 2 Laboratoire Bordelais de Recherche en Informatique
• 3 Laboratoire d'informatique Algorithmique : Fondements et Applications
• 4 Laboratoire d'Informatique Gaspard-Monge
• 5 Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]

This article presents a methodology that automatically derives a combinatorial specification for the permutation class $\mathcal{C} = Av(B)$, given its basis $B$ of excluded patterns and the set of simple permutations in $\mathcal{C}$, 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 $\mathcal{C}$, this system being always positive and algebraic. It also yields a uniform random sampler of permutations in $\mathcal{C}$. The method presented is fully algorithmic.