Upper bounding the coefficients of Tutte polynomials with a variable fixed

Source abstract

The Tutte polynomial is a fundamental invariant of graphs and matroids. For a matroid M of rank r, the Tutte polynomial T_M(x,y) of M serves as a generalization of the characteristic polynomial chi_M(x), with the relationship given by chi_M(x) = (-1)^r T_M(1-x,0). For any real number t satisfying 0 = r + c_g, thereby giving a partial affirmative answer to the question of extending their upper bound beyond binary matroids.