{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T07:14:13Z","timestamp":1747898053363,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2019,3]]},"abstract":"<jats:p> A plane tiling by the copies of a polyomino is called isohedral if every pair of copies in the tiling has a symmetry of the tiling that maps one copy to the other. We show that, for every [Formula: see text]-omino (i.e., polyomino consisting of [Formula: see text] cells), the number of non-equivalent isohedral tilings generated by 90 degree rotations, so called p4-tilings or quarter-turn tilings, is bounded by a constant (independent of [Formula: see text]). The proof relies on the analysis of the factorization of the boundary word of a polyomino. We also show an example of a polyomino that has three non-equivalent p4-tilings. <\/jats:p>","DOI":"10.1142\/s0218195919400016","type":"journal-article","created":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T03:31:31Z","timestamp":1566271891000},"page":"3-19","source":"Crossref","is-referenced-by-count":1,"title":["On the Number of p4-Tilings by an n-Omino"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2322-6072","authenticated-orcid":false,"given":"Kazuyuki","family":"Amano","sequence":"first","affiliation":[{"name":"Department of Computer Science, Gunma University, 1-5-1 Tenjin, Kiryu, Gunma 376-8515, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshinobu","family":"Haruyama","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Gunma University, 1-5-1 Tenjin, Kiryu, Gunma 376-8515, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,8,20]]},"reference":[{"key":"S0218195919400016BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00026-N"},{"key":"S0218195919400016BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574705"},{"key":"S0218195919400016BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/11907350_34"},{"key":"S0218195919400016BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2008.05.026"},{"key":"S0218195919400016BIB005","first-page":"463","volume":"2","author":"Erd\u0151s P.","year":"1935","journal-title":"Comp. Math."},{"key":"S0218195919400016BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0174934-9"},{"key":"S0218195919400016BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-007-0719-y"},{"key":"S0218195919400016BIB008","doi-asserted-by":"publisher","DOI":"10.3390\/sym3040828"},{"key":"S0218195919400016BIB009","doi-asserted-by":"publisher","DOI":"10.1051\/ita:2007012"},{"key":"S0218195919400016BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8566-0"},{"key":"S0218195919400016BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100053810"},{"key":"S0218195919400016BIB014","first-page":"29","volume-title":"Proc. 21st Canadian Conf. Computational Geometry (CCCG 2009)","author":"Horiyama T.","year":"2009"},{"volume-title":"The 7th Annual Meeting of Asian Association for Algorithms and Computation (AAAC 2014)","year":"2014","author":"Horiyama T.","key":"S0218195919400016BIB015"},{"first-page":"50:1","volume-title":"Proc. 32nd Int. Symp. Computational Geometry (SoCG 2016)","author":"Langerman S.","key":"S0218195919400016BIB016"},{"key":"S0218195919400016BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48971-0_1"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195919400016","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T03:31:36Z","timestamp":1566271896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195919400016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3]]},"references-count":15,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,8,20]]},"published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.1142\/S0218195919400016"],"URL":"https:\/\/doi.org\/10.1142\/s0218195919400016","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"type":"print","value":"0218-1959"},{"type":"electronic","value":"1793-6357"}],"subject":[],"published":{"date-parts":[[2019,3]]}}}