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Lower Bounds for Partial Matchings in Regular Bipartite Graphs and Applications to the Monomer–Dimer Entropy

Published online by Cambridge University Press:  01 May 2008

SHMUEL FRIEDLAND  and
LEONID GURVITS
SHMUEL FRIEDLAND
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA (e-mail: friedlan@uic.edu)
LEONID GURVITS
Affiliation:
Los Alamos National Laboratories, Los Alamos, NM 87545, USA (e-mail: gurvits@lanl.gov)
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Abstract

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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 347 - 361
Copyright
Copyright © Cambridge University Press 2007

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