Vol. 8, No. 3, 2015

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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

We develop theorems to compute the p-colorability of the families of T(m,n,r,s) twisted torus knots for n ±1(modm) 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.

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knot theory, determinants, colorability, twisted torus knots
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 11C20, 05C15
Received: 10 November 2009
Revised: 27 June 2013
Accepted: 17 November 2013
Published: 5 June 2015

Communicated by Kenneth S. Berenhaut
Matt DeLong
Department of Mathematics
Taylor University
236 West Reade Avenue
Upland, IN 46989
United States
Matthew Russell
Department of Mathematics
Rutgers, The State University of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854
United States
Jonathan Schrock
Oak Ridge National Laboratory
P.O. Box 2008 MS6164
Oak Ridge, TN 37831
United States