{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:43Z","timestamp":1753893823939,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given a family of lattice polytopes, a common endeavor in Ehrhart theory is the classification of those polytopes in the family that are Gorenstein, or more generally level. In this article, we consider these questions for ${\\boldsymbol s}$-lecture hall polytopes, which are a family of simplices arising from $\\mathbf {s}$-lecture hall partitions. In particular, we provide concrete classifications for both of these properties purely in terms of ${\\boldsymbol s}$-inversion sequences. Moreover, for a large subfamily of ${\\boldsymbol s}$-lecture hall polytopes, we provide a more geometric classification of the Gorenstein property in terms of\u00a0 its tangent cones. We then show how one can use the classification of level ${\\boldsymbol s}$-lecture hall polytopes to construct infinite families of level ${\\boldsymbol s}$-lecture hall polytopes, and to describe level ${\\boldsymbol s}$-lecture hall polytopes in small dimensions.<\/jats:p>","DOI":"10.37236\/8626","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:18Z","timestamp":1599187638000},"source":"Crossref","is-referenced-by-count":1,"title":["Level Algebras and $\\mathbf {s}$-Lecture Hall Polytopes"],"prefix":"10.37236","volume":"27","author":[{"given":"Florian","family":"Kohl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"McCabe","family":"Olsen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,9,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p50\/8168","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p50\/8168","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:18Z","timestamp":1599187638000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,4]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8626","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,9,4]]},"article-number":"P3.50"}}