{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:27Z","timestamp":1753893807267,"version":"3.41.2"},"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>We give a bijective proof of the Aztec diamond theorem, stating that there\u00a0are $2^{n(n+1)\/2}$ domino tilings of the Aztec diamond of order $n$. The\u00a0proof in fact establishes a similar result for non-intersecting families of\u00a0$n+1$ Schr\u00f6der paths, with horizontal, diagonal or vertical steps, linking\u00a0the grid points of two adjacent sides of an $n\\times n$ square grid; these\u00a0families are well known to be in bijection with tilings of the Aztec\u00a0diamond. Our bijection is produced by an invertible \"combing'' algorithm,\u00a0operating on families of paths without non-intersection condition, but\u00a0instead with the requirement that any vertical steps come at the end of a\u00a0path, and which are clearly $2^{n(n+1)\/2}$ in number; it transforms them into\u00a0non-intersecting families.<\/jats:p>","DOI":"10.37236\/2809","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:12:30Z","timestamp":1578705150000},"source":"Crossref","is-referenced-by-count":7,"title":["A Bijection Proving the Aztec Diamond Theorem by Combing Lattice Paths"],"prefix":"10.37236","volume":"20","author":[{"given":"Fr\u00e9d\u00e9ric","family":"Bosio","sequence":"first","affiliation":[]},{"given":"Marc A. A.","family":"Van Leeuwen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,11,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:49Z","timestamp":1579259449000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,29]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/2809","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,11,29]]},"article-number":"P24"}}