176 citations · 1.3k across the 156 of their papers we have counts for
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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.…
An Affine Index Polynomial Invariant of Virtual Knots
Louis H. Kauffman
This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an es…
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…