Affiliation:
1. Center for Mathematical Analysis, Geometry, and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Abstract
In this article we present the following new fact for prime p = 11. For knots 62 and 72, mincol11 62 = 5 = mincol11 72, along with the following feature. There is a pair of diagrams, one for 62 and the other one for 72, each of them admitting only non-trivial 11-colorings using five colors, but neither of them admitting being colored with the sets of five colors that color the other one. This new fact is in full contrast with the behavior exhibited by links admitting non-trivial p-colorings over the smaller primes, p = 2, 3, 5 or 7. We also prove results concerning obstructions to the minimization of colors over generic odd moduli. We apply these to finding the right colors to eliminate from non-trivial colorings. We thus prove that 5 is the minimum number of colors for each knot of prime determinant 11 or 13 from Rolfsen's table.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
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