{"paper":{"title":"On the size of lattice simplices with a single interior lattice point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Gennadiy Averkov","submitted_at":"2011-03-03T09:41:28Z","abstract_excerpt":"Let $\\mathcal{T}^d(1)$ be the set of all $d$-dimensional simplices $T$ in $\\real^d$ with integer vertices and a single integer point in the interior of $T$. It follows from a result of Hensley that $\\mathcal{T}^d(1)$ is finite up to affine transformations that preserve $\\mathbb{Z}^d$. It is known that, when $d$ grows, the maximum volume of the simplices $T \\in \\cT^d(1)$ becomes extremely large. We improve and refine bounds on the size of $T \\in \\mathcal{T}^d(1)$ (where by the size we mean the volume or the number of lattice points). It is shown that each $T \\in \\mathcal{T}^d(1)$ can be decompo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0629","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"}