{"paper":{"title":"Ehrhart polynomials of partial permutohedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Roger E. Behrend","submitted_at":"2024-03-11T17:58:43Z","abstract_excerpt":"For positive integers $m$ and $n$, the partial permutohedron $\\mathcal{P}(m,n)$ is a certain integral polytope in $\\mathbb{R}^m$, which can be defined as the convex hull of the vectors from $\\{0,1,\\ldots,n\\}^m$ whose nonzero entries are distinct. For $n=m-1$, $\\mathcal{P}(m,m-1)$ is (after translation by $(1,\\ldots,1)$) the polytope $P_m$ of parking functions of length $m$, and for $n\\ge m$, $\\mathcal{P}(m,n)$ is combinatorially equivalent to an $m$-stellohedron. The main result of this paper is an explicit expression for the Ehrhart polynomial of $\\mathcal{P}(m,n)$ for any $m$ and $n$ with $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06975","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.06975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}