Simple permutations: Decidability and unavoidable substructures

We prove that it is decidable whether a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains an alternation or oscillation of length k. Key words: permutation class, restricted permutation, simple permutation 1991 MSC: 03B25, 03D05, 05A15, 68F10, 68Q45

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Robert Brignall, Nikola Ruskuc, Vincent Vatter
• Keywords: Permutation, Permutation Class, Simple Permutation, TCS 2008, Theoretical Computer Science