{"paper":{"title":"Universal conditions on $h^*$-vectors of lattice simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani","submitted_at":"2018-12-25T15:33:14Z","abstract_excerpt":"In this paper, we will prove that given a lattice simplex with its $h^*$-polynomial $\\sum_{i \\geq 0}h_i^*t^i$, if $h_{k+1}^*=\\cdots=h_{2k}^*=0$ holds, then there exists a lattice simplex of degree $k$ whose $h^*$-polynomial coincides with $\\sum_{i=0}^k h_i^*t^i$. Moreover, we will present the examples showing that the condition $h_{k+1}^*=h_{k+2}^*=\\cdots=h_{2k-1}^*=0$ is necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10123","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":""},"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"}