2013/08/28 by Pedro Lopes, Lopes, Pedro · 1 citation
Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27
paper · pdf · doi:10.48550/arxiv.1308.6054
Version accepted in JKTR
openalex publication_date 2013/08/28 · arxiv created 2015/04/08 · arxiv updated 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 5 colors, but neither of them admitting being colored with the sets of 5 colors that color the other one. This 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 find 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.