{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T19:42:03Z","timestamp":1649014923048},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Knot Theory Ramifications"],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p>This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant.<\/jats:p><jats:p>Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely.<\/jats:p><jats:p>We are thus led to conjecture that for each prime p there exists a unique positive integer, m<jats:sub>p<\/jats:sub>, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determinant of L and the modulus r, the minimum number of colors of L modulo r is m<jats:sub>p<\/jats:sub>.<\/jats:p>","DOI":"10.1142\/s0218216511009728","type":"journal-article","created":{"date-parts":[[2011,5,12]],"date-time":"2011-05-12T01:42:56Z","timestamp":1305164576000},"page":"1250025","source":"Crossref","is-referenced-by-count":12,"title":["MINIMUM NUMBER OF FOX COLORS FOR SMALL PRIMES"],"prefix":"10.1142","volume":"21","author":[{"given":"PEDRO","family":"LOPES","sequence":"first","affiliation":[{"name":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Portugal"},{"name":"Department of Mathematics, Instituto Superior T\u00e9cnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]},{"given":"JO\u00c3O","family":"MATIAS","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Instituto Superior T\u00e9cnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9935-6"},{"key":"rf2","unstructured":"R. H.\u00a0Fox, Topology of 3-Manifolds and Related Topics, ed. M. K.\u00a0Fort\u00a0Jr. (Prentice-Hall, 1962)\u00a0pp. 120\u2013167."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0634"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/4256"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2006.11.006"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0691-0"},{"key":"rf7","series-title":"Carus Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.5948\/UPO9781614440239","volume-title":"Knot Theory","author":"Livingston C.","year":"1993"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216503002378"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2009.9.2027"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/06230963"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216510008480"},{"key":"rf13","first-page":"939","volume":"46","author":"Satoh S.","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\/S0218216511009728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T02:51:35Z","timestamp":1592535095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218216511009728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":12,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.1142\/S0218216511009728"],"URL":"https:\/\/doi.org\/10.1142\/s0218216511009728","relation":{},"ISSN":["0218-2165","1793-6527"],"issn-type":[{"value":"0218-2165","type":"print"},{"value":"1793-6527","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}