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Communication Dans Un Congrès Année : 2012

Refined enumeration of permutations sorted with two stacks and a D_8-symmetry

Résumé

We study permutations that are sorted by operators of the form $\mathbf{S} \circ \alpha \circ \mathbf{S}$, where $\mathbf{S}$ is the usual stack sorting operator introduced by D. Knuth and $\alpha$ is any $D_8$-symmetry obtained combining the classical reverse, complement and inverse operations. Such permutations can be characterized by excluded (generalized) patterns. Some conjectures about the enumeration of these permutations, refined with numerous classical statistics, have been proposed by A. Claesson, M. Dukes and E. Steingrímsson. We prove these conjectures, and enrich one of them with a few more statistics. The proofs mostly rely on generating trees techniques, and on a recent bijection of S. Giraudo between Baxter and twisted Baxter permutations.

Dates et versions

hal-00749260 , version 1 (07-11-2012)

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Citer

Mathilde Bouvel, Olivier Guibert. Refined enumeration of permutations sorted with two stacks and a D_8-symmetry. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), Jul 2012, Nagoya, Japan. pp.757-768. ⟨hal-00749260⟩

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