Slavik Jablan, Louis H. Kauffman, Pedro Lopes. On the Maximum Number of Colors for Links

Natural Sciences / Mathematics / Geometry

Submitted on: Sep 18, 2012, 07:00:56

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.

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