{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T01:39:05Z","timestamp":1648863545446},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> We introduce a new method for computing the word length of an element of Thompson's group F with respect to a \"consecutive\" generating set of the form X<jats:sub>n<\/jats:sub> = {x<jats:sub>0<\/jats:sub>,x<jats:sub>1<\/jats:sub>, \u2026,x<jats:sub>n<\/jats:sub>}, which is a subset of the standard infinite generating set for F. We use this method to show that (F, X<jats:sub>n<\/jats:sub>) is not almost convex, and has pockets of increasing, though bounded, depth dependent on n. <\/jats:p>","DOI":"10.1142\/s0218196709005445","type":"journal-article","created":{"date-parts":[[2010,1,28]],"date-time":"2010-01-28T10:30:36Z","timestamp":1264674636000},"page":"963-997","source":"Crossref","is-referenced-by-count":1,"title":["COMPUTING WORD LENGTH IN ALTERNATE PRESENTATIONS OF THOMPSON'S GROUP F"],"prefix":"10.1142","volume":"19","author":[{"given":"MATTHEW","family":"HORAK","sequence":"first","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science, University of Wisconsin-Stout, Menomonie, WI 54751, USA"}]},{"given":"MELANIE","family":"STEIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Trinity College, Hartford, CT 06106, USA"}]},{"given":"JENNIFER","family":"TABACK","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670500261X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02671613"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388451"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181266"},{"key":"rf5","first-page":"291","volume":"31","author":"Cannon J.","journal-title":"Geom. Dedicata"},{"key":"rf6","first-page":"215","volume":"42","author":"Cannon J. W.","journal-title":"Enseign. Math."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08043-3"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00516-7"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03375-0"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/hah030"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024971818319"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670400192X"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005025418287"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003347"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01264925"},{"key":"rf18","author":"Thiel C.","journal-title":"Bonner Math. Schriften"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005445","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:21:26Z","timestamp":1565130086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":16,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1142\/S0218196709005445"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005445","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}