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On the Validations of the Asymptotic Matching Conjectures
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA; Berlin Mathematical School, Berlin, Germany.
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA .
Department of Physics, AlbaNova University Center, KTH, 106 91, Stockholm, Sweden .
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2008 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 133, no 3, 513-533 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p is an element of[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.

Place, publisher, year, edition, pages
Springer, 2008. Vol. 133, no 3, 513-533 p.
Keyword [en]
matching and asymptotic growth of average matchings for r-regular bipartite graphs, monomer-dimer partitions and entropies, monomer-dimer problem, regular bipartite graphs, series-expansion, lattice, entropy, number, matrices, systems
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-52124DOI: 10.1007/S10955-008-9550-YISI: 000260376300006OAI: oai:DiVA.org:umu-52124DiVA: diva2:497228
Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2017-12-07Bibliographically approved

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Lundow, Per-HåkanMarkström, Klas
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