{"paper":{"title":"Ehrhart polynomials of integral simplices with prime volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani","submitted_at":"2011-07-25T08:05:48Z","abstract_excerpt":"For an integral convex polytope $\\Pc \\subset \\RR^N$ of dimension $d$, we call $\\delta(\\Pc)=(\\delta_0, \\delta_1,..., \\delta_d)$ the $\\delta$-vector of $\\Pc$ and $\\vol(\\Pc)=\\sum_{i=0}^d\\delta_i$ its normalized volume. In this paper, we will establish the new equalities and inequalities on $\\delta$-vectors for integral simplices whose normalized volumes are prime. Moreover, by using those, we will classify all the possible $\\delta$-vectors of integral simplices with normalized volume 5 and 7."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4862","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"}