Broken Circuit Theorem for Assigning Polynomials of Regular Matroids

Recently, we have introduced assigning polynomials of regular matroids that count nowhere-zero chains over finite Abelian groups associated with homomorphisms. The well-known broken circuit theorem of Whitney evaluates the coefficients of characteristic polynomials of graphs and matroids. In this paper, we generalize the approach of broken circuits to determine the coefficients of assigning polynomials of regular matroids.