{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822166,"version":"3.41.2"},"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>A tatami tiling is an arrangement of $1 \\times 2$ dominoes (or mats) in a rectangle with $m$ rows and $n$ columns, subject to the constraint that no four corners meet at a point. For fixed $m$ we present and use Dean Hickerson's combinatorial decomposition of the set of tatami tilings \u2014 a decomposition that allows them to be viewed as certain classes of restricted compositions when $n \\ge m$. Using this decomposition we find the ordinary generating functions of both unrestricted and inequivalent tatami tilings that fit in a rectangle with $m$ rows and $n$ columns, for fixed $m$ and $n \\ge m$. This allows us to verify a modified version of a conjecture of Knuth. Finally, we give explicit solutions for the count of tatami tilings, in the form of sums of binomial coefficients.<\/jats:p>","DOI":"10.37236\/215","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:24:36Z","timestamp":1578716676000},"source":"Crossref","is-referenced-by-count":5,"title":["Counting Fixed-Height Tatami Tilings"],"prefix":"10.37236","volume":"16","author":[{"given":"Frank","family":"Ruskey","sequence":"first","affiliation":[]},{"given":"Jennifer","family":"Woodcock","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,10,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r126\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r126\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:19Z","timestamp":1579315219000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/215","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,10,12]]},"article-number":"R126"}}