Combinatorial specification of permutation classes

Details Combinatorial specification of permutation classes Combinatorial specification of permutation classes

2012-04-03

arxiv.org/abs/1204.0797v1

Mathematics

Combinatorics

Scientific paper

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.

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