{"paper":{"title":"Hermite normal forms and $\\delta$-vector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Nan Li, Takayuki Hibi","submitted_at":"2010-09-30T01:14:25Z","abstract_excerpt":"Let $\\delta(\\Pc) = (\\delta_0, \\delta_1,..., \\delta_d)$ be the $\\delta$-vector of an integral polytope $\\Pc \\subset \\RR^N$ of dimension $d$. Following the previous work of characterizing the $\\delta$-vectors with $\\sum_{i=0}^d \\delta_i \\leq 3$, the possible $\\delta$-vectors with $\\sum_{i=0}^d \\delta_i = 4$ will be classified. And each possible $\\delta$-vectors can be obtained by simplices. We get this result by studying the problem of classifying the possible integral simplices with a given $\\delta$-vector $(\\delta_0, \\delta_1,..., \\delta_d)$, where $\\sum_{i=0}^d \\delta_i \\leq 4$, by means of H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6023","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"}