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- Title
ON THE MAXIMUM NUMBER OF COLORS FOR LINKS.
- Authors
JABLAN, SLAVIK; KAUFFMAN, LOUIS H.; LOPES, PEDRO
- Abstract
For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of colors, mod p, 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 any Schubert Normal Form (SNF) of it, modulo its determinant, which uses all colors available. If this determinant is an odd prime, then any non-trivial coloring of this SNF, modulo the determinant, uses all available colors. We prove also that the number of crossings in the SNF equals twice the determinant of the link minus 2. Facts about torus links and their coloring abilities are also proved.
- Subjects
LINK theory; NUMBER theory; TORUS; KNOT theory; INTEGERS; MATHEMATICAL transformations
- Publication
Journal of Knot Theory & Its Ramifications, 2013, Vol 22, Issue 3, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216513500132