3 papers
math.GT2026
Three formulas for the Ising and Potts invariants of a knot or link
Tristan Bullock, Thomas Kindred
Jones described how the Ising and Potts models from statistical mechanics give rise, with appropriate choices of Boltzmann weights, to invariants of an oriented link. The Boltzmann…
math.GT2025
Crosscap numbers of alternating links via state codes
Isaias Bahena, Thomas Kindred, Jason Parsley
We describe a way of encoding a Kauffman state as a set of tuples, similar to a Gauss code. Then we describe a procedure for using these state codes to determine the unoriented gen…
math.GT2025
Average crosscap number of a 2-bridge knot
Moshe Cohen, Thomas Kindred, Adam M. Lowrance +2
We determine a simple condition on a particular state graph of an alternating knot or link diagram that characterizes when the unoriented genus and crosscap number coincide, extend…