{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T10:13:23Z","timestamp":1781345603222,"version":"3.54.1"},"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>We show that every heptagon is a section of a $3$-polytope with $6$ vertices.\u00a0This implies that every $n$-gon with $n\\geq 7$ can be obtained as a section of a\u00a0$(2+\\lfloor\\frac{n}{7}\\rfloor)$-dimensional polytope with at most $\\lceil\\frac{6n}{7}\\rceil$ vertices; and\u00a0provides a geometric proof of the fact that every nonnegative\u00a0$n\\times m$ matrix of rank $3$ has nonnegative\u00a0rank not larger than $\\lceil\\frac{6\\min(n,m)}{7}\\rceil$. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122,\u00a02014).<\/jats:p>","DOI":"10.37236\/4315","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:32:27Z","timestamp":1578684747000},"source":"Crossref","is-referenced-by-count":8,"title":["Polygons as Sections of Higher-Dimensional Polytopes"],"prefix":"10.37236","volume":"22","author":[{"given":"Arnau","family":"Padrol","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julian","family":"Pfeifle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2015,2,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:45Z","timestamp":1579239465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4315","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,9]]},"article-number":"P1.24"}}