Simple permutations poset

Adeline Pierrot (1) , Dominique Rossin (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This article studies the poset of simple permutations with respect to the pattern involvement. We specify results on critically indecomposable posets obtained by Schmerl and Trotter in [11] to simple permutations and prove that if σ, π are two simple permutations such that π < σ then there exists a chain of simple permutations σ^(0) = σ, σ^(1) , . . . , σ^(k) = π such that |σ^(i) | − |σ^(i+1) | = 1 - or 2 when permutations are exceptional- and σ^(i+1) < σ^(i) . This characterization induces an algorithm polynomial in the size of the output to compute the simple permutations in a wreath-closed permutation class.

Domaines: Combinatoire [math.CO]

Adeline Pierrot, Dominique Rossin. Simple permutations poset. 2011. ⟨hal-00649396⟩