{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T21:02:39Z","timestamp":1773262959812,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,2]]},"abstract":"<jats:p>Andrews and Curtis conjectured in 1965 that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. Recent computational work by Miasnikov and Myasnikov on this problem has been based on genetic algorithms. We show that a computational attack based on a breadth-first search of the tree of equivalent presentations is also viable, and seems to outperform that based on genetic algorithms. It allows us to extract shorter proofs (in some cases, provably shortest) and to consider the length thirteen case for two generators. We prove that, up to equivalence, there is a unique minimum potential counterexample.<\/jats:p>","DOI":"10.1142\/s0218196703001365","type":"journal-article","created":{"date-parts":[[2003,3,27]],"date-time":"2003-03-27T09:28:57Z","timestamp":1048757337000},"page":"61-68","source":"Crossref","is-referenced-by-count":15,"title":["BREADTH-FIRST SEARCH AND THE ANDREWS\u2013CURTIS CONJECTURE"],"prefix":"10.1142","volume":"13","author":[{"given":"GEORGE","family":"HAVAS","sequence":"first","affiliation":[{"name":"Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072, Australia"}]},{"given":"COLIN","family":"RAMSAY","sequence":"additional","affiliation":[{"name":"Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(85)90010-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0173241-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/25.6.513"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700036388"},{"key":"rf5","first-page":"167","volume":"48","author":"Grattan-Guinness I.","journal-title":"Notices Amer. Math. Soc."},{"key":"rf7","series-title":"Andrews\u2013Curtis and Todd\u2013Coxeter proof words","volume-title":"Group St. Andrews 2001 in Oxford","author":"Havas G."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196799000370"},{"key":"rf9","doi-asserted-by":"crossref","unstructured":"A. D.\u00a0Miasnikov and A. G.\u00a0Myasnikov, Groups and Computation III, Balanced presentations of the trivial group on two generators and the Andrews\u2013Curtis conjecture\u00a08, eds. W. M.\u00a0Kantor and A.\u00a0Seress (Ohio State Math. Res. Inst. Publ. 8, de Gruyter, Berlin, 2001)\u00a0pp. 257\u2013263.","DOI":"10.1515\/9783110872743.257"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/250\/03848"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1975-0380813-5"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T15:28:00Z","timestamp":1704814080000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":10,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,2]]}},"alternative-id":["10.1142\/S0218196703001365"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001365","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}