{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:43:45Z","timestamp":1773258225290,"version":"3.50.1"},"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>For lattice polytopes $P_1,\\ldots, P_k \\subseteq \\mathbb{R}^d$, Bihan (2016) introduced the discrete mixed volume $DMV(P_1,\\dots,P_k)$ in analogy to the classical mixed volume.\u00a0 In this note we study the associated mixed Ehrhart polynomial $ME_{P_1, \\dots,P_k}(n) = DMV(nP_1, \\dots, nP_k)$.\u00a0 We provide a characterization of all mixed Ehrhart coefficients in terms of the classical multivariate Ehrhart polynomial. Bihan (2016) showed that the discrete mixed volume is always non-negative. Our investigations yield simpler proofs for certain special cases.We also introduce and study the associated mixed $h^*$-vector. We show that for large enough dilates $r\u00a0 P_1, \\ldots, rP_k$ the corresponding mixed $h^*$-polynomial has only real roots and as a consequence\u00a0 the mixed $h^*$-vector becomes non-negative.\u00a0<\/jats:p>","DOI":"10.37236\/5815","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:39:16Z","timestamp":1578667156000},"source":"Crossref","is-referenced-by-count":4,"title":["Mixed Ehrhart polynomials"],"prefix":"10.37236","volume":"24","author":[{"given":"Christian","family":"Haase","sequence":"first","affiliation":[]},{"given":"Martina","family":"Juhnke-Kubitzke","sequence":"additional","affiliation":[]},{"given":"Raman","family":"Sanyal","sequence":"additional","affiliation":[]},{"given":"Thorsten","family":"Theobald","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,1,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:06:32Z","timestamp":1579219592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/5815","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,20]]},"article-number":"P1.10"}}