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Article overview
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Minimal sufficient sets of colors and minimum number of colors | Jun Ge
; Xian'an Jin
; Louis H. Kauffman
; Pedro Lopes
; Lianzhu Zhang
; | Date: |
11 Jan 2015 | Abstract: | In this paper we first investigate minimal sufficient sets of colors for p=11
and 13. For odd prime p and any p-colorable link L with non-zero determinant,
we give alternative proofs of mincol_p L geq 5 for p geq 11 and mincol_p L
geq 6 for p geq 17. We elaborate on equivalence classes of sets of distinct
colors (on a given modulus) and prove that there are two such classes of five
colors modulo 11, and only one such class of five colors modulo 13. Finally, we
give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh
concerning an inequality involving crossing numbers. We show it is an equality
only for the trefoil and for the figure-eight knots. | Source: | arXiv, 1501.2421 | Services: | Forum | Review | PDF | Favorites |
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