{
  "id": "1810.02255",
  "version": "v1",
  "published": "2018-10-04T14:52:18.000Z",
  "updated": "2018-10-04T14:52:18.000Z",
  "title": "A combinatorial formula for the Ehrhart $h^{*}$-vector of the hypersimplex",
  "authors": [
    "Donghyun Kim"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a combinatorial formula for the Ehrhart $h^*$-vector of the hypersimplex. In particular, we show that $h^{*}_{d}(\\Delta_{k,n})$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T14:52:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial formula",
      "hypersimplex",
      "hypersimplicial decorated ordered set partitions",
      "general conjecture",
      "generic cross-section"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}