Brignall, Robert; Ruškuc, Nik and Vatter, Vincent
Simple permutations: Decidability and unavoidable substructures.
Theoretical Computer Science, 391(1-2),
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.
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