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Characterization of the OU matrix of a braid diagram

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arxiv 2502.16035 v3 pith:LWZDLWGC submitted 2025-02-22 math.GT

Ayaka Shimizu , Yoshiro Yaguchi This is my paper · ORCID
classification math.GT
keywords matrixbraidstrandscharacterizeddiagrampureapplicationbraids
verification ladder T0 review T1 audit T2 compute T3 formal
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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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  1. The CN matrix of a pure braid projection

    math.GT 2025-06 conditional novelty 6.0 of 10

    An even symmetric 6x6 matrix is the crossing-count matrix of a pure 6-braid projection exactly when it satisfies the T0 condition.

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