{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T03:43:47Z","timestamp":1648784627808},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> Given a countable set X (usually taken to be \u2115 or \u2124), an infinite permutation \u03c0 of X is a linear ordering \u227a<jats:sub>\u03c0<\/jats:sub> of X, introduced in [6]. This paper investigates the combinatorial complexity of infinite permutations on \u2115 associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map. An upper bound for the complexity is found for general words, and a formula for the complexity is established for the Sturmian words and the Thue-Morse word. <\/jats:p>","DOI":"10.1142\/s0129054112400680","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T02:34:43Z","timestamp":1363746883000},"page":"1653-1675","source":"Crossref","is-referenced-by-count":1,"title":["PERMUTATION COMPLEXITY AND THE LETTER DOUBLING MAP"],"prefix":"10.1142","volume":"23","author":[{"given":"STEVEN","family":"WIDMER","sequence":"first","affiliation":[{"name":"Mathematics Department, University of North Texas, Denton, Texas 76203, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,3,19]]},"reference":[{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)90274-E"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01762232"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2007.04.017"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(89)90013-3"},{"key":"p_9","first-page":"304","volume":"3","author":"Makarov M.A.","year":"2006","journal-title":"Mat. Izv."},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/s11202-009-0076-6"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.03.038"},{"key":"p_12","first-page":"1","volume":"1","author":"Thue A.","year":"1912","journal-title":"Selsk. Skr. Mat. Nat. Kl."},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2010.08.002"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054112400680","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:26:44Z","timestamp":1565094404000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054112400680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":9,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2013,3,19]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S0129054112400680"],"URL":"https:\/\/doi.org\/10.1142\/s0129054112400680","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}