Generalized Friedland-Tverberg inequality: applications and extensions

Details Generalized Friedland-Tverberg inequality: applications and extensions Generalized Friedland-Tverberg inequality: applications and extensions

2006-03-16

arxiv.org/abs/math/0603410v2

Mathematics

Combinatorics

21 pages, 2 figures

Scientific paper

We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It is shown that some of these bounds are asymptotically sharp. We improve the known lower bound for the three dimensional monomer-dimer entropy. We present Ryser-like formulas for computations of matchings in bipartite and general graphs. Additional algorithmic applications are given.

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