The CN matrix of a pure braid projection

2025/06/10 by Ozawa, Yuko, Ayaka Shimizu, Shimizu, Ayaka +2 · 2 citations
Mathematics · Computer Science · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.08659

Abstract

The CN matrix of an n-braid projection B is an n × n matrix such that each (i,j) entry indicates the number of crossings between i^th and j^th strands of B. In this paper, several patterns of an n × n matrix to be a CN matrix are discussed, and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized.

Citations

• Characterization of the OU matrix of a braid diagram
• Determinant of the OU matrix of a braid diagram
• A note on the unknotting number and the region unknotting number of weaving knots
• ALGORITHMS FOR POSITIVE BRAIDS

Cited by

• The crossing matrix and the extended first Johnson homomorphism of a braid group
• Determinant of the crossing matrix of a braid

Related

• Characterization of the OU matrix of a braid diagram
• Crossing Matrices of Positive Braids
• Determinant of the crossing matrix of a braid
• Determinant of the OU matrix of a braid diagram
• Matrix transposition and braid reversion