The rank of a warping matrix

摘要

The warping matrix has been defined for knot projections and knot diagrams by using warping degrees, and the warping matrix of a knot diagram represents the knot diagram uniquely. In this paper we show that the rank of a warping matrix is one greater than the crossing number of the knot projection or diagram. We also discuss the linearly independence of knot diagrams by considering the warping incidence matrices. (C) 2016 Elsevier B.V. All rights reserved.