Change search
ReferencesLink to record
Permanent link

Direct link
On the Validations of the Asymptotic Matching Conjectures
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Condensed Matter Theory.
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
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
URN: urn:nbn:se:kth:diva-17911DOI: 10.1007/s10955-008-9550-yISI: 000260376300006ScopusID: 2-s2.0-54949158545OAI: diva2:335956
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Lundow, Per Håkan
By organisation
Condensed Matter Theory
In the same journal
Journal of statistical physics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 28 hits
ReferencesLink to record
Permanent link

Direct link