Counting Knot Mosaics with ALLSAT (Student Abstract)

Abstract Knot mosaics are a model of a quantum knot system. A knot mosaic is a m-by-n grid where each location on the grid may contain any of 11 possible tiles such that the final layout has closed loops. Oh et al. proved a recurrence relation of state matrices to count the number of m-by-n knot mosaics. Our contribution is to use ALLSAT solvers to count knot mosaics and to experimentally try different ways to encode the AT MOST ONE constraint in SAT. We plan to use our SAT method as a tool to list knot mosaics of interest for specific classes of knots.