5 citations · 5 across the 12 of their papers we have counts for
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The crossing matrix and the Burau matrix of pure braids
Ayaka Shimizu, Yoshiro Yaguchi
We show that the first derivative of the Burau matrix at coincides with the Laplacian of the crossing matrix for pure braids. We also discuss conjugacy invariants derived fro…
Cabled braids and their crossing matrices
Ayaka Shimizu, Yoshiro Yaguchi
We study cabling operations on braids, and characterize the matrices that can be realized as crossing matrices of reducible pure braids. We also use cabling to construct enhanced c…
Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence
Ayaka Shimizu, Yoshiro Yaguchi
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surfac…
The crossing matrix and the extended first Johnson homomorphism of a braid group
Yusuke Kuno, Yoshiro Yaguchi
We compare two crossed homomorphisms on a braid group, one defined diagrammatically and the other defined algebraically. We show that these crossed homomorphisms are essentially th…
The CN matrix of a pure braid projection
Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi
The CN matrix of an -braid projection is an matrix such that each entry indicates the number of crossings between and strands of .…
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…
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 called the up-down action. In this paper, w…
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…
A note on the cross-index of a complete graph based on a linear tree
Yusuke Gokan, Hayato Katsumata, Katsuya Nakajima +2
In this paper it is shown that a complete graph with vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maxim…
Up-down colorings of virtual-link diagrams and the necessity of Reidemeister moves of type II
Kanako Oshiro, Ayaka Shimizu, Yoshiro Yaguchi
We introduce an up-down coloring of a virtual-link diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between tw…
Biquandle Virtual Brackets
Sam Nelson, Kanako Oshiro, Ayaka Shimizu +1
We introduce an infinite family of quantum enhancements of the biquandle counting invariant we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle co…
Axis systems of link projections
Kirara Horiguchi, Ayaka Shimizu, Ryohei Watanabe +1
An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characte…