Séminaire Lotharingien de Combinatoire, 82B.4 (2019), 12 pp.

Donghyun Kim

A combinatorial formula for the Ehrhart h*-vector of the hypersimplex

Abstract. We give a combinatorial formula for the Ehrhart h*-vector of the hypersimplex. In particular, we show that h*d(Δk,n) is the number of hypersimplicial decorated ordered set partitions of type (k,n) with winding number d, thereby proving a conjecture of Nick Early. We do this by proving a more general conjecture of Nick Early on the Ehrhart h*-vector of a generic cross-section of a hypercube.

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

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