{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:56:23Z","timestamp":1759838183924,"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>Let $\\mathcal{P} \\subset \\mathbb{R}^{n}$ be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the $k$th dilate of $\\mathcal{P}$ ($k$ a positive integer) is a quasi-polynomial function of $k$ \u2014 that is, a \"polynomial\" in which the coefficients are themselves periodic functions of $k$. It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values.<\/jats:p>","DOI":"10.37236\/6059","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:36:22Z","timestamp":1578670582000},"source":"Crossref","is-referenced-by-count":2,"title":["Periods of Ehrhart Coefficients of Rational Polytopes"],"prefix":"10.37236","volume":"25","author":[{"given":"Tyrrell B.","family":"McAllister","sequence":"first","affiliation":[]},{"given":"H\u00e9l\u00e8ne O.","family":"Rochais","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p64\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p64\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:37:35Z","timestamp":1579235855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6059","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,16]]},"article-number":"P1.64"}}