Bounds on the permanent and some applications
  We give new lower and upper bounds on the permanent of a doubly stochastic matrix. Combined with previous work, this improves on the deterministic approximation factor for the permanent.   We also give a combinatorial application of the lower bound, proving S. Friedland's "Asymptotic Lower Matching Conjecture" for the monomer-dimer problem. 
Leonid Gurvits and Alex Samorodnitsky
math.CO