{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810813,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If $P\\subset {\\Bbb R}^d$ is a rational polytope, then $i_P(t):=\\#(tP\\cap {\\Bbb Z}^d)$ is a quasi-polynomial in $t$, called the Ehrhart quasi-polynomial of $P$.  A period of $i_P(t)$ is ${\\cal D}(P)$, the smallest ${\\cal D}\\in {\\Bbb Z}_+$ such that ${\\cal D}\\cdot P$ has integral vertices.  Often, ${\\cal D}(P)$ 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 $P\\subset{\\Bbb R}^d$ 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 polynomial.  We conjecture that, for fixed $d$, there is a polynomial time algorithm to compute the minimum period of $i_P(t)$. The tools we use are rational generating functions.<\/jats:p>","DOI":"10.37236\/1931","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:13Z","timestamp":1578719473000},"source":"Crossref","is-referenced-by-count":20,"title":["Computing the Period of an Ehrhart Quasi-Polynomial"],"prefix":"10.37236","volume":"12","author":[{"given":"Kevin","family":"Woods","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,7,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:48:11Z","timestamp":1579322891000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1931","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,7,29]]},"article-number":"R34"}}