{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:33:29Z","timestamp":1762299209935,"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>Recent work has focused on the roots $z\\in\\mathbb{C}$ of the Ehrhart polynomial of a lattice polytope $P$. The case when $\\Re{z}=-1\/2$ is of particular interest: these polytopes satisfy Golyshev's \"canonical line hypothesis\". We characterise such polytopes when $\\mathrm{dim}(P)\\leq 7$. We also consider the \"half-strip condition\", where all roots $z$ satisfy $-\\mathrm{dim}(P)\/2\\leq\\Re{z}\\leq \\mathrm{dim}(P)\/2-1$, and show that this holds for any reflexive polytope with $\\mathrm{dim}(P)\\leq 5$. We give an example of a $10$-dimensional reflexive polytope which violates the half-strip condition, thus improving on an example by Ohsugi\u2013Shibata in dimension $34$.<\/jats:p>","DOI":"10.37236\/7780","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:11:48Z","timestamp":1578640308000},"source":"Crossref","is-referenced-by-count":4,"title":["Ehrhart Polynomial Roots of Reflexive Polytopes"],"prefix":"10.37236","volume":"26","author":[{"given":"G\u00e1bor","family":"Heged\u00fcs","sequence":"first","affiliation":[]},{"given":"Akihiro","family":"Higashitani","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Kasprzyk","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p38\/7797","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p38\/7797","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:16:17Z","timestamp":1579234577000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7780","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,3,8]]},"article-number":"P1.38"}}