9 citations · 21 across the 6 of their papers we have counts for
19 papers · 1 filter
Set Theoretic Yang-Baxter Solutions via Fox Calculus
J. Scott Carter, Masahico Saito
We construct solutions to the set-theoretic Yang-Baxter equation using braid group representations in free group automorphisms and their Fox differentials. The method resembles the…
A lower bound for the number of Reidemeister moves of type III
J. Scott Carter, Mohamed Elhamdadi, Masahico Saito +1
We study the number of Reidemeister type III moves using Fox n-colorings of knot diagrams.
Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules
J. Scott Carter, Masahico Saito
This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and…
Ribbon concordance of surface-knots via quandle cocycle invariants
J. Scott Carter, Masahico Saito, Shin Satoh
We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the i…
Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
J. Scott Carter, Mohamed Elhamdadi, Matias Graña +1
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the cas…
Homology Theory for the Set-Theoretic Yang-Baxter Equation and Knot Invariants from Generalizations of Quandles
J. Scott Carter, Mohamed Elhamdadi, Masahico Saito
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.