{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T12:33:23Z","timestamp":1773405203077,"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>We construct a combinatorial model that is described by the cube recurrence, a quadratic recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in ${\\Bbb Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky about the structure of these polynomials, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences, including the Somos-6 and Somos-7 sequences.  We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.<\/jats:p>","DOI":"10.37236\/1826","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:31:37Z","timestamp":1578709897000},"source":"Crossref","is-referenced-by-count":27,"title":["The Cube Recurrence"],"prefix":"10.37236","volume":"11","author":[{"given":"Gabriel D.","family":"Carroll","sequence":"first","affiliation":[]},{"given":"David","family":"Speyer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,10,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r73\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r73\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:53:21Z","timestamp":1579323201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r73"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1826","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10,18]]},"article-number":"R73"}}