2014/05/29 by Hugh Howards, Howards, Hugh, Andrew Kobin +1
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.1405.7683
Knot mosaics are used to model physical quantum states. The mosaic number of a knot is the smallest integer m such that the knot can be represented as a knot m-mosaic. In this paper we establish an upper bound for the crossing number of a knot in terms of the mosaic number. Given an m-mosaic and any knot K that is represented on the mosaic, its crossing number c is bounded above by (m - 2)2 - 2 if m is odd, and (m - 2)2 - (m - 3) if m is even.