{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:53Z","timestamp":1753893773849,"version":"3.41.2"},"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>The paper considers ribbon tilings of large regions and their per-tile entropy (the logarithm of the number of tilings divided by the number of tiles). For tilings of general regions by tiles of length $n$, we give an upper bound on the per-tile entropy as $n - 1$. For growing rectangular regions,\u00a0 we prove the existence of the asymptotic per tile entropy and show that it is bounded from below by $\\log_2 (n\/e)$ and from above by $\\log_2(en)$. For growing generalized \"Aztec Diamond\" regions and for growing \"stair\" regions, the asymptotic per-tile entropy is calculated exactly as $1\/2$ and $\\log_2(n + 1) - 1$, respectively.<\/jats:p>","DOI":"10.37236\/10991","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:36Z","timestamp":1682076876000},"source":"Crossref","is-referenced-by-count":0,"title":["On Enumeration and Entropy of Ribbon Tilings"],"prefix":"10.37236","volume":"30","author":[{"given":"Yinsong","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladislav","family":"Kargin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,4,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:37Z","timestamp":1682076877000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i2p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,21]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/10991","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,4,21]]},"article-number":"P2.15"}}