Coboundaries, Flows, and Tutte Polynomials of Matrices

Using matroid duality and the critical problem, we show that certain evaluations of the Tutte polynomial of a matroid represented as a matrix over a finite field GF(q) can be interpreted as weighted sums over pairs f; g of functions defined from the ground set to GF(q) whose difference f g is the restriction of a linear functional on the column space of the matrix. Similar interpretations are given for the characteristic polynomial evaluated at q. These interpre-tations extend and elaborate interpretations for Tutte and chromatic polynomials of graphs due to Goodall and Matiyasevich