Séminaire Lotharingien de Combinatoire, 82B.11 (2019), 12 pp.

Sam Hopkins

The CDE property for skew vexillary permutations

Abstract. We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies more generally to certain "skew vexillary" permutations (a notion we introduce), and shows that these posets are in fact "toggle CDE." As a corollary we obtain a homomesy result for rowmotion acting on semidistributive lattices in the sense of Barnard and of Thomas and Williams.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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