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

2018/10/04 by Dong-Hyun Kim, Kim, Donghyun
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1810.02255

Abstract

We give a combinatorial formula for the Ehrhart h^*-vector of the hypersimplex. In particular, we show that h^*_d(Δ_k,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.

Related

• Conjectures for Ehrhart h^*-vectors of Hypersimplices and Dilated Simplices
• Equivariant Ehrhart Theory of Hypersimplices
• Ehrhart h^*-vectors of hypersimplices
• The h^*-polynomials of type C hypersimplices
• The Ehrhart series of alcoved polytopes