Characterization of the OU matrix of a braid diagram

2025/02/22 by Shimizu, Ayaka, Yaguchi, Yoshiro · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2502.16035

Abstract

The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram is characterized for up to 5 strands. As an application, the crossing matrix of a positive pure braid is also characterized for up to 5 strands. Moreover, a standard form of the OU matrix is given and characterized for general braids of up to 5 strands.

Cited by

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

Related

• Determinant of the OU matrix of a braid diagram
• The CN matrix of a pure braid projection
• Crossing Matrices of Positive Braids
• Determinant of the crossing matrix of a braid
• A Laundry Surface for Braids