{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:41:43Z","timestamp":1775839303145,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An integral convex polytope $\\mathcal{P} \\subset \\mathbb{R}^N$ possesses the integer\u00a0decomposition property if, for any integer $k &gt; 0$ and for\u00a0any $\\alpha \\in k \\mathcal{P} \\cap \\mathbb{Z}^{N}$, there exist $\\alpha_{1}, \\ldots,\u00a0\\alpha_k \\in \\mathcal{P} \\cap \\mathbb{Z}^{N}$ such that $\\alpha = \\alpha_{1}\u00a0+ \\cdots + \\alpha_k$. A fundamental question is to determine the\u00a0integers $k &gt; 0$ for which the dilated polytope $k\\mathcal{P}$ possesses the\u00a0integer decomposition property. In the present paper, combinatorial\u00a0invariants related to the integer decomposition property of dilated\u00a0polytopes will be proposed and studied.<\/jats:p>","DOI":"10.37236\/4204","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:52:48Z","timestamp":1578703968000},"source":"Crossref","is-referenced-by-count":27,"title":["Integer Decomposition Property of Dilated Polytopes"],"prefix":"10.37236","volume":"21","author":[{"given":"David A.","family":"Cox","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Haase","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takayuki","family":"Hibi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akihiro","family":"Higashitani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,11,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:40:47Z","timestamp":1579257647000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,6]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4204","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,6]]},"article-number":"P4.28"}}