{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T19:55:48Z","timestamp":1718135748095},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,2]]},"abstract":"<jats:p> Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form. <\/jats:p>","DOI":"10.1142\/s0218196717500059","type":"journal-article","created":{"date-parts":[[2017,1,17]],"date-time":"2017-01-17T06:03:10Z","timestamp":1484632990000},"page":"61-105","source":"Crossref","is-referenced-by-count":1,"title":["The relaxation normal form of braids is regular"],"prefix":"10.1142","volume":"27","author":[{"given":"Vincent","family":"Jug\u00e9","sequence":"first","affiliation":[{"name":"Mines ParisTech, PSL \u2013 Research University, 75272 Paris Cedex 06, France"},{"name":"Universit\u00e9 Paris Diderot, Sorbonne Paris Cit\u00e9, IRIF, UMR 8243, CNRS, 75205 Paris, France"},{"name":"LSV, CNRS &amp; ENS Cachan, Universit\u00e9 Paris-Saclay, France"}]}],"member":"219","published-online":{"date-parts":[[2017,2,16]]},"reference":[{"key":"S0218196717500059BIB001","doi-asserted-by":"publisher","DOI":"10.2307\/1969218"},{"key":"S0218196717500059BIB002","series-title":"Annals of Mathematical Studies","volume-title":"Braids, Links and Mapping Class Groups","author":"Birman J.","year":"1974"},{"key":"S0218196717500059BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216508006373"},{"issue":"6","key":"S0218196717500059BIB005","first-page":"633","volume":"315","author":"Dehornoy P.","year":"1992","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"S0218196717500059BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1214782-4"},{"key":"S0218196717500059BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/148"},{"key":"S0218196717500059BIB008","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/98"},{"key":"S0218196717500059BIB009","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"S0218196717500059BIB010","doi-asserted-by":"publisher","DOI":"10.1515\/9781400839049"},{"key":"S0218196717500059BIB011","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1999.191.49"},{"key":"S0218196717500059BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:49:49Z","timestamp":1565095789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2]]},"references-count":11,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2017,2,16]]},"published-print":{"date-parts":[[2017,2]]}},"alternative-id":["10.1142\/S0218196717500059"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500059","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2]]}}}