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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 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…
math.GT2024
Warping labeling for twisted knots and twisted virtual braids
Komal Negi, Ayaka Shimizu, Madeti Prabhakar
In this paper, we introduce the concept of the warping degree for twisted knots, construct an invariant for them, and utilize it to establish a labeling scheme for these knots, kno…