Characterization of the OU matrix of a braid diagram
Geometric Topology
2025-07-22 v3
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.
Cite
@article{arxiv.2502.16035,
title = {Characterization of the OU matrix of a braid diagram},
author = {Ayaka Shimizu and Yoshiro Yaguchi},
journal= {arXiv preprint arXiv:2502.16035},
year = {2025}
}
Comments
22 pages, 17 figures