3 citations
7 papers
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…
Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions
Wen-Xiu Ma, Yuncheng You
A broad set of sufficient conditions consisting of systems of linear partial differential equations is presented which guarantees that the Wronskian determinant solves the Korteweg…
Complexiton solutions to integrable equations
Wen-Xiu Ma
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential…
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.
The Affinity of a Permutation of a Finite Vector Space
W. Edwin Clark, Xiang-dong Hou, Alec Mihailovs
For a permutation f of an n-dimensional vector space V over a finite field of order q we let k-affinity(f) denote the number of k-flats X of V such that f(X) is also a k-flat. By k…
Limits of Zeros of Orthogonal Polynomials on the Circle
Barry Simon, Vilmos Totik
We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding…