2023/08/04 by Baldridge, Scott, Kauffman, Louis H., McCarty, Ben · 1 citation
#05C10 #05C15 #05C31 #05C70 #57K16 #57M15 #57R56 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2308.02732
The total face color polynomial is based upon the Poincaré polynomials of a family of filtered n-color homologies. It counts the number of n-face colorings of ribbon graphs for each positive integer n. As such, it may be seen as a successor of the Penrose polynomial, which at n=3 counts 3-edge colorings (and consequently 4-face colorings) of planar trivalent graphs. In this paper we describe a state sum formula for the polynomial. This formula unites two different perspectives about graph coloring: one based upon topological quantum field theory and the other on diagrammatic tensors.