Complete monotonicity for inverse powers of some combinatorially defined polynomials
Complete monotonicity for inverse powers of some combinatorially defined polynomials
We prove the complete monotonicity on (0,∞)n for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of Szegő and answers, among other things, a long-standing question of Lewy and Askey concerning the …