{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T12:44:12Z","timestamp":1777207452067,"version":"3.51.4"},"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>Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e.  those polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word $W$ may be factorized as $W = XY\\overline{X} \\,\\overline{Y}$. In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of $psp$-polyominoes with a fixed planar basis according to the semi-perimeter. The case of pseudo-square convex polyominoes is also analyzed.<\/jats:p>","DOI":"10.37236\/1041","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:03:44Z","timestamp":1578701024000},"source":"Crossref","is-referenced-by-count":7,"title":["Tilings by Translation: Enumeration by a Rational Language Approach"],"prefix":"10.37236","volume":"13","author":[{"given":"Srecko","family":"Brlek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Frosini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simone","family":"Rinaldi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Vuillon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2006,2,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:26:06Z","timestamp":1579303566000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1041","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2,15]]},"article-number":"R15"}}