Ayaka Shimizu

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20242026

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math.GT2025

Determinant of the crossing matrix of a braid

Ayaka Shimizu

In this paper, we define a braid invariant, the purified determinant $P (b)$ of a braid $b$ , considering the determinant of the crossing matrix of a pure braid derived from $b$ , and…

math.GT2025

The CN matrix of a pure braid projection

Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi

The CN matrix of an $n$ -braid projection $B$ is an $n \times n$ matrix such that each $(i, j)$ entry indicates the number of crossings between $i^{t h}$ and $j^{t h}$ strands of $B$ .…

math.GT2025

Characterization of the OU matrix of a braid diagram

Ayaka Shimizu, Yoshiro Yaguchi

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…