We prove a new efficiently computable lower bound on the coefficients of stable homogeneous polynomials and present its algorthmic and combinatorial applications. Our main application is the first poly-time deterministic algorithm which approximates the partition functions associated with
boolean matrices with prescribed row and (uniformly bounded) column sums within simply exponential multiplicative factor. This new algorithm is a particular instance of
new polynomial time
deterministic algorithms related to the multiple partial differentiation of polynomials given by evaluation oracles

A journal version, most of the typos are fixed.

We prove a new efficiently computable lower bound on the coefficients of stable homogeneous polynomials and present its algorthmic and combinatorial applications. Our main application is the first poly-time deterministic algorithm which approximates the partition functions associated with
boolean matrices with prescribed row and (uniformly bounded) column sums within simply exponential multiplicative factor. This new algorithm is a particular instance of
new polynomial time
deterministic algorithms related to the multiple partial differentiation of polynomials given by evaluation oracles