{"paper":{"title":"The Minimum Period of the Ehrhart Quasi-polynomial of a Rational Polytope","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kevin M. Woods, Tyrrell B. McAllister","submitted_at":"2003-10-16T22:52:15Z","abstract_excerpt":"If $P\\subset \\R^d$ is a rational polytope, then $i_P(n):=#(nP\\cap \\Z^d)$ is a quasi-polynomial in $n$, called the Ehrhart quasi-polynomial of $P$. The period of $i_P(n)$ must divide $\\LL(P)= \\min \\{n \\in \\Z_{> 0} \\colon nP \\text{is an integral polytope}\\}$. Few examples are known where the period is not exactly $\\LL(P)$. We show that for any $\\LL$, there is a 2-dimensional triangle $P$ such that $\\LL(P)=\\LL$ but such that the period of $i_P(n)$ is 1, that is, $i_P(n)$ is a polynomial in $n$. We also characterize all polygons $P$ such that $i_P(n)$ is a polynomial. In addition, we provide a cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310255","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"}