Conjectures for Ehrhart $h^{\ast }$-vectors of Hypersimplices and Dilated Simplices

Abstract

We formulate conjectures giving combinatorial interpretations of the Ehrhart $h^{\ast }$-vector, for hypersimplices, for dilated simplices and for generic cross-sections of cubes, in terms of certain decorated ordered set partitions. All were formulated and checked computationally during our graduate study at Penn State.

References in corpus (2)

• Combinatorics and Representation Theory for Generalized Permutohedra I: Simplicial Plates
• On the inner structure of a permutation: Bicolored Partitions and Eulerians, Trees and Primitives