{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T13:02:54Z","timestamp":1648904574498},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Knot Theory Ramifications"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> For each prime p &gt; 7 we obtain the expression for an upper bound on the minimum number of colors needed to non-trivially color T(2, p), the torus knot of type (2, p), modulo p. This expression is t + 2l -1 where t and l are extracted from the prime p. It is obtained from iterating the so-called Teneva transformations which we introduced in a previous article. With the aid of our estimate we show that the ratio \"number of colors needed vs. number of colors available\" tends to decrease with increasing modulus p. For instance as of prime 331, the number of colors needed is already one tenth of the number of colors available. Furthermore, we prove that 5 is the minimum number of colors needed to non-trivially color T(2, 11) modulo 11. Finally, as a preview of our future work, we prove that 5 is the minimum number of colors modulo 11 for two rational knots with determinant 11. <\/jats:p>","DOI":"10.1142\/s0218216512501258","type":"journal-article","created":{"date-parts":[[2012,8,12]],"date-time":"2012-08-12T20:38:13Z","timestamp":1344803893000},"page":"1250125","source":"Crossref","is-referenced-by-count":6,"title":["THE TENEVA GAME"],"prefix":"10.1142","volume":"21","author":[{"given":"LOUIS H.","family":"KAUFFMAN","sequence":"first","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St., Chicago IL 60607-7045, USA"}]},{"given":"PEDRO","family":"LOPES","sequence":"additional","affiliation":[{"name":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior T\u00e9cnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2013,2,4]]},"reference":[{"key":"rf1","volume-title":"Introduction to Knot Theory","author":"Crowell R.","year":"2008"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0634"},{"key":"rf3","first-page":"357","volume":"49","author":"Kauffman L. H.","journal-title":"Enseign. Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2006.11.006"},{"key":"rf5","first-page":"111","volume":"11","author":"Kauffman L. H.","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216511009728"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2009.9.2027"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/06230963"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216510008480"},{"key":"rf10","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\/S0218216512501258","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T09:00:00Z","timestamp":1565082000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218216512501258"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":10,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2013,2,4]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S0218216512501258"],"URL":"https:\/\/doi.org\/10.1142\/s0218216512501258","relation":{},"ISSN":["0218-2165","1793-6527"],"issn-type":[{"value":"0218-2165","type":"print"},{"value":"1793-6527","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}