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math.GT2026
The Penrose-Kauffman Polynomial
Louis H. Kauffman, Daniel S. Silver, Susan G. Williams
For any cubic graph in a closed orientable surface and a perfect matching, the Penrose-Kauffman polynomial is a sum of chromatic polynomials of a collection of associated graphs. A…
math.GT2025
Generalised Biracks and the Birack Polynomial Invariant
Andrew Bartholomew, Roger Fenn, Louis Kauffman
We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring inva…
math.GT2004★ 2 cited
Virtual Knot Theory --Unsolved Problems
Roger Fenn, Louis H. Kauffman, Vassily O. Manturov
This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.