{"paper":{"title":"Ehrhart polynomials with negative coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Akiyoshi Tsuchiya, Koutarou Yoshida, Takayuki Hibi","submitted_at":"2015-06-01T12:16:06Z","abstract_excerpt":"It is shown that, for each $d \\geq 4$, there exists an integral convex polytope $\\mathcal{P}$ of dimension $d$ such that each of the coefficients of $n, n^{2}, \\ldots, n^{d-2}$ of its Ehrhart polynomial $i(\\mathcal{P},n)$ is negative. Moreover, it is also shown that for each $d \\geq 3$ and $1 \\leq k \\leq d-2$, there exists an integral convex polytope $\\mathcal{P}$ of dimension $d$ such that the coefficient of $n^k$ of the Ehrhart polynomial $i(\\mathcal{P},n)$ of $\\mathcal{P}$ is negative and all its remaining coefficients are positive. Finally, we consider all the possible sign patterns of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00467","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}