{"paper":{"title":"Computing the period of an Ehrhart quasi-polynomial","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kevin M. Woods","submitted_at":"2004-11-09T17:55:30Z","abstract_excerpt":"If P is a rational polytope in R^d, then $i_P(t):=#(tP\\cap Z^d)$ is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P. A period of i_P(t) is D(P), the smallest positive integer D such that D*P has integral vertices. Often, D(P) is the minimum period of i_P(t), but, in several interesting examples, the minimum period is smaller. We prove that, for fixed d, there is a polynomial time algorithm which, given a rational polytope P in R^d and an integer n, decides whether n is a period of i_P(t). In particular, there is a polynomial time algorithm to decide whether i_P(t) is a polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411207","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"}