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arXiv · 1002.3866

Deciding the finiteness of the number of simple permutations contained in a wreath-closed class is polynomial

Frédérique Bassino·Mathilde Bouvel·Adeline Pierrot·Dominique Rossin
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Abstract

We present an algorithm running in time O(n ln n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall, Ruskuc and Vatter which presents a decision procedure (of high complexity) for solving this question, without the assumption that Av(B) is wreath-closed. Using combinatorial, algorithmic and language theoretic arguments together with one of our previous results on pin-permutations, we are able to transform the problem into a co-finiteness problem in a complete deterministic automaton.

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Frédérique Bassino, Mathilde Bouvel, Adeline Pierrot, Dominique Rossin. 2010-02-20. Deciding the finiteness of the number of simple permutations contained in a wreath-closed class is polynomial. https://arxiv.org/abs/1002.3866

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