{"paper":{"title":"Existence of regular unimodular triangulations of dilated empty simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Koutarou Yoshida, Takayuki Hibi","submitted_at":"2017-01-10T08:33:17Z","abstract_excerpt":"Given integers $k$ and $m$ with $k \\geq 2$ and $m \\geq 2$, let $P$ be an empty simplex of dimension $(2k-1)$ whose $\\delta$-polynomial is of the form $1+(m-1)t^k$. In the present paper, the necessary and sufficient condition for the $k$-th dilation $kP$ of $P$ to have a regular unimodular triangulation will be presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02471","kind":"arxiv","version":3},"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"}