{"paper":{"title":"Integer decomposition property of dilated polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Christian Haase, David A. Cox, Takayuki Hibi","submitted_at":"2012-11-25T10:48:50Z","abstract_excerpt":"Let $\\mathcal{P} \\subset \\mathbb{R}^N$ be an integral convex polytope of dimension $d$ and write $k \\mathcal{P}$, where $k = 1, 2, \\ldots$, for dilations of $\\mathcal{P}$. We say that $\\mathcal{P}$ possesses the integer decomposition property if, for any integer $k = 1, 2, \\ldots$ and for any $\\alpha \\in k \\mathcal{P} \\cap \\mathbb{Z}^N$, there exist $\\alpha_{1}, \\ldots, \\alpha_k$ belonging to $\\mathcal{P} \\cap \\mathbb{Z}^N$ such that $\\alpha = \\alpha_1 + \\cdots + \\alpha_k$. A fundamental question is to determine the integers $k > 0$ for which the dilated polytope $k\\mathcal{P}$ possesses the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5755","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"}