{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T20:28:50Z","timestamp":1648844930867},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Knot Theory Ramifications"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p> In this article we present the following new fact for prime p = 11. For knots 6<jats:sub>2<\/jats:sub> and 7<jats:sub>2<\/jats:sub>, mincol<jats:sub>11<\/jats:sub> 6<jats:sub>2<\/jats:sub> = 5 = mincol<jats:sub>11<\/jats:sub> 7<jats:sub>2<\/jats:sub>, along with the following feature. There is a pair of diagrams, one for 6<jats:sub>2<\/jats:sub> and the other one for 7<jats:sub>2<\/jats:sub>, each of them admitting only non-trivial 11-colorings using five colors, but neither of them admitting being colored with the sets of five colors that color the other one. This new fact is in full contrast with the behavior exhibited by links admitting non-trivial p-colorings over the smaller primes, p = 2, 3, 5 or 7. We also prove results concerning obstructions to the minimization of colors over generic odd moduli. We apply these to finding the right colors to eliminate from non-trivial colorings. We thus prove that 5 is the minimum number of colors for each knot of prime determinant 11 or 13 from Rolfsen's table. <\/jats:p>","DOI":"10.1142\/s0218216515500273","type":"journal-article","created":{"date-parts":[[2015,4,13]],"date-time":"2015-04-13T09:44:52Z","timestamp":1428918292000},"page":"1550027","source":"Crossref","is-referenced-by-count":4,"title":["The minimization of the number of colors is different at p = 11"],"prefix":"10.1142","volume":"24","author":[{"given":"Pedro","family":"Lopes","sequence":"first","affiliation":[{"name":"Center for Mathematical Analysis, Geometry, and Dynamical Systems, Department of Mathematics, Instituto Superior T\u00e9cnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2015,5,25]]},"reference":[{"key":"rf1","volume-title":"Introduction to Knot Theory","author":"Crowell R.","year":"2008"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498812500089"},{"key":"rf3","unstructured":"J.\u00a0Ge, Knots in Poland III, Banach Center Publications\u00a0103, eds. J.\u00a0Przytycki and P.\u00a0Traczyk (Institute of Mathematics, Polish Academy of Sciences, 2014)\u00a0pp. 63\u201376."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0634"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/1971403"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2006.11.006"},{"key":"rf9","first-page":"17","volume":"21","author":"Kauffman L. H.","year":"2012","journal-title":"J. Knot Theory Ramifications"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216511009728"},{"key":"rf11","first-page":"91","volume":"59","author":"Nakamura T.","year":"2013","journal-title":"Yokohama Math. J."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/06230963"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/346"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216510008480"},{"key":"rf15","first-page":"939","volume":"46","author":"Satoh S.","year":"2009","journal-title":"Osaka J. Math."}],"container-title":["Journal of Knot Theory and Its Ramifications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218216515500273","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:24:51Z","timestamp":1565148291000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218216515500273"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":13,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2015,5,25]]},"published-print":{"date-parts":[[2015,4]]}},"alternative-id":["10.1142\/S0218216515500273"],"URL":"https:\/\/doi.org\/10.1142\/s0218216515500273","relation":{},"ISSN":["0218-2165","1793-6527"],"issn-type":[{"value":"0218-2165","type":"print"},{"value":"1793-6527","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}