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

We present an algorithm running in time O(n log n) which decides if a wreathclosed 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 [9] 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 [6], we are able to transform the problem into a co-finiteness problem in a complete deterministic automaton.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Frédérique Bassino, Mathilde Bouvel, Adeline Pierrot, Dominique Rossin
• Keywords: CORR 2010, Education, Finite Basis, Finite Number, Permutation Class