Characterization of the OU matrix of a braid diagram

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.

Publication Details

Journal
ArXiv.org
Published
2025-02-22
Primary Topic
Geometric and Algebraic Topology
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article
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Characterization of the OU matrix of a braid diagram

ArXiv.org
Geometric and Algebraic Topology
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Characterization of the OU matrix of a braid diagram

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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.

ArXiv.org
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Geometric and Algebraic Topology
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Characterization of the OU matrix of a braid diagram · ArXiv.org (2025) | TGRS Research Map | TGRS