176 citations · 1.3k across the 156 of their papers we have counts for
8 papers · 2 filters
A Linking Number Definition of the Affine Index Polynomial and Applications
Lena C. Folwaczny, Louis H. Kauffman
This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial.…
Local moves on knots and products of knots
Louis H. Kauffman, Eiji Ogasa
We show several relations between local moves on 1-dimensional knots and those on high dimensional knots related by products of knots.
Equivalence Classes of Colorings
Jun Ge, Slavik Jablan, Louis H. Kauffman +1
For any link and for any modulus we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of t…
Book Review of "Virtual Knot Theory - The State of the Art" by Vassily Manturov and Denis Ilyutko, World Scientific (2012), ISBN: 978-981-4401-12-8
Louis H. Kauffman
This article is a review of the book "Virtual Knot Theory - The State of the Art" by Vassily Manturov and Denis Ilyutko, World Scientific (2012), ISBN: 978-981-4401-12-8.
A Graphical Construction of the sl(3) Invariant for Virtual Knots
Louis Hirsch Kauffman, Vassily Olegovich Manturov
By generalizing the Kuperberg sl(3) bracket, we construct a graph-valued analogue of the Homflypt sl(3) invariant for virtual knots. The restriction of this invariant for classical…
On the Maximum Number of Colors for Links
Slavik Jablan, Louis H. Kauffman, Pedro Lopes
For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-t…
The Teneva Game
Louis Kauffman, Pedro Lopes
For each prime p > 7 we obtain the expression for an upper bound on the minimum number of colors needed to non-trivially color T(2, p), the torus knots of type (2, p), modulo p. Th…
Following Knots Down Their Energy Gradients
Louis H. Kauffman
This paper details a series of experiments in searching for minimal energy configurations for knots and links using the computer program KnotPlot. The most interesting phenomena fo…