{"paper":{"title":"Roots of Ehrhart polynomials of Gorenstein Fano polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Hidefumi Ohsugi, Takayuki Hibi","submitted_at":"2010-01-23T15:58:22Z","abstract_excerpt":"Given arbitrary integers $k$ and $d$ with $0 \\leq 2k \\leq d$, we construct a Gorenstein Fano polytope $\\Pc \\subset \\RR^d$ of dimension $d$ such that (i) its Ehrhart polynomial $i(\\Pc, n)$ possesses $d$ distinct roots; (ii) $i(\\Pc, n)$ possesses exactly $2k$ imaginary roots; (iii) $i(\\Pc, n)$ possesses exactly $d - 2k$ real roots; (iv) the real part of each of the imaginary roots is equal to $- 1 / 2$; (v) all of the real roots belong to the open interval $(-1, 0)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4165","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/1001.4165/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"}