Slavik Jablan, Louis H. Kauffman, Pedro Lopes. On the Maximum Number of Colors for Links
Submitted on: Sep 18, 2012, 07:00:56
Natural Sciences / Mathematics / Geometry
Description: For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-trivial p-coloring with any number of colors, from the minimum to the maximum number of colors. Furthermore, for any rational link, we prove that there exists a non-trivial coloring of a 2-bridge diagram of it, modulo its determinant, which uses all colors available. If this determinant is an odd prime, then any non-trivial coloring of the 2-bridge diagram, modulo the determinant, uses all available colors. Facts about torus links and their colorability are also proved.
The abstract of this article will be published in the September 2012 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.
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