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Colorability and
determinants of $T(m,n,r,s)$ twisted torus knots for
$n\equiv\pm 1\pmod m$
Matt DeLong, Matthew Russell and Jonathan Schrock
Vol. 8 (2015), No. 3, 361–384
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Abstract |
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We develop theorems to compute the -colorability of the families of twisted torus knots for by finding their determinants. Instead of the usual method of reducing crossing matrices to find the determinant, we describe a new method that is applicable for braid representations with full cycles and twists. |
Keywords
knot theory, determinants, colorability, twisted torus
knots
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 11C20, 05C15
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Milestones
Received: 10 November 2009
Revised: 27 June 2013
Accepted: 17 November 2013
Published: 5 June 2015
Communicated by Kenneth S. Berenhaut
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Authors |
| Matt DeLong | |
| Department of Mathematics Taylor University 236 West Reade Avenue Upland, IN 46989 United States |
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| Matthew Russell | |
| Department of Mathematics Rutgers, The State University of New Jersey 110 Frelinghuysen Road Piscataway, NJ 08854 United States |
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| Jonathan Schrock | |
| Oak Ridge National Laboratory P.O. Box 2008 MS6164 Oak Ridge, TN 37831 United States |
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