Séminaire Lotharingien de Combinatoire, 86B.25 (2022), 12 pp.

Elena Tielker

Weighted Ehrhart Series and a Type B Analogue of a Formula of MacMahon

Abstract. We present a formula for the joint distribution of major index and descent statistic on signed multiset permutations. It allows a description in terms of the h^*-polynomial of a certain polytope. We associate a family of polytopes to (generalised) permutations of types A and B. We use this connection to study properties of the (generalised) Eulerian numbers, such as palindromicity and unimodality, by identifying certain properties of the associated polytope.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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