{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:44:02Z","timestamp":1774277042519,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We demonstrate a natural bijection between a subclass of alternating sign matrices (ASMs) defined by a condition on the corresponding monotone triangle which we call the gapless condition and a subclass of totally symmetric self-complementary plane partitions defined by a similar condition on the corresponding fundamental domains or Magog triangles. We prove that, when restricted to permutations, this class of ASMs reduces to 312-avoiding permutations. This leads us to generalize pattern avoidance on permutations to a family of words associated to ASMs, which we call Gog words.  We translate the gapless condition on monotone triangles into a pattern avoidance-like condition on Gog words associated.  We estimate the number of gapless monotone triangles using a bijection with $p$-branchings.<\/jats:p>","DOI":"10.37236\/2022","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:36:36Z","timestamp":1578713796000},"source":"Crossref","is-referenced-by-count":9,"title":["Monotone Triangles and 312 Pattern Avoidance"],"prefix":"10.37236","volume":"18","author":[{"given":"Arvind","family":"Ayyer","sequence":"first","affiliation":[]},{"given":"Robert","family":"Cori","sequence":"additional","affiliation":[]},{"given":"Dominique","family":"Gouyou-Beauchamps","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,11,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p26\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:59:10Z","timestamp":1579301950000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i2p26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/2022","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11,7]]},"article-number":"P26"}}