Mosaic number of knots

Author:

Lee Hwa Jeong1,Hong Kyungpyo2,Lee Ho1,Oh Seungsang2

Affiliation:

1. Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea

2. Department of Mathematics, Korea University, Anam-dong, Sungbuk-ku, Seoul 136-701, Korea

Abstract

Lomonaco and Kauffman developed knot mosaics to give a definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot n-mosaic is an n × n matrix of 11 kinds of specific mosaic tiles representing a knot or a link. The mosaic number m(K) of a knot K is the smallest integer n for which K is representable as a knot n-mosaic. In this paper, we establish an upper bound on the mosaic number of a knot or a link K in terms of the crossing number c(K). Let K be a nontrivial knot or a non-split link except the Hopf link. Then m(K) ≤ c(K) + 1. Moreover if K is prime and non-alternating except [Formula: see text] link, then m(K) ≤ c(K) - 1.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 14 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

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