5 papers
A counterexample for the polar conjecture of Spencer-Brown
Scott Baldridge, Louis H. Kauffman, Ben McCarty
In 1976, George Spencer-Brown announced a proof of the four color theorem, using operations on Tait colorings for trivalent plane graphs. In subsequent work he formulated these ope…
Categorification of Chromatic, Dichromatic and Penrose Polynomials
Louis H Kauffman
This paper discusses ways to categorify chromatic, dichromatic and Penrose polynomials, including categorifications of integer evaluations of chromatic polynomials. We show that wi…
Primes Between Squares -- Commentary on Appendix 8 of Laws Of Form
J. M. Flagg, Louis H. Kauffman, Divyamaan Sahoo
This paper provides a commentary and guide to Appendix 8 of Laws Of Form, which is a chapter (appendix) on number theory in the book Laws of Form by Spencer-Brown. (Spencer-Brown,L…
The clock theorem for knotoids and linkoids
Neslihan Gügümcü, Louis H. Kauffman
In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in . The clock theorem implies that clock states of a knotoid diagram form a lattice…
Fusion and Fission of Particle-like Chiral Nematic Vortex Knots
Darian Hall, Jung-Shen Benny Tai, Louis H. Kauffman +1
Vortex knots have been seen decaying in many physical systems. Here we describe topologically protected vortex knots, which remain stable and undergo fusion and fission while conse…