Conjectures for Ehrhart h^*-vectors of Hypersimplices and Dilated Simplices

2017/10/26 by Nick Early, Early, Nick
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1710.09507

openalex publication_date 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate conjectures giving combinatorial interpretations of the Ehrhart h^*-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.

Citations

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

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