Ayaka Shimizu

collaborators

5 papers

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…

math.GT2024

Orbits by the up-down action of braid diagrams

Komal Negi, Ayaka Shimizu, Yoshiro Yaguchi +1

The set of all virtual or classical braid diagrams forms a monoid and gives a natural monoid action on a direct product of $Z$ called the up-down action. In this paper, w…

math.GT2024

Determinant of the OU matrix of a braid diagram

Ayaka Shimizu, Yoshiro Yaguchi

In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the deter…