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. © 2007 Elsevier Ltd. All rights reserved.
Brignall, R., Ruškuc, N., & Vatter, V. (2008). Simple permutations: Decidability and unavoidable substructures. Theoretical Computer Science, 391(1–2), 150–163. https://doi.org/10.1016/j.tcs.2007.10.037