Characterization of the OU matrix of a braid diagram

Ayaka Shimizu; Yoshiro Yaguchi

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arXiv · 2502.16035

Characterization of the OU matrix of a braid diagram

Ayaka Shimizu·Yoshiro Yaguchi

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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.

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Ayaka Shimizu, Yoshiro Yaguchi. 2025-02-22. Characterization of the OU matrix of a braid diagram. https://arxiv.org/abs/2502.16035

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