Theory of computation of multidimensional entropy with an application to the monomer–dimer problem

Friedland, Shmuel; Peled, Uri N.

doi:10.1016/j.aam.2004.08.005

Cited by 37 publications

(115 citation statements)

References 37 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…See for example [1,2,4,5,6,12,14,15,16,17,19,20,21,23,24,25,26,28,30]. Let G = (V, E) be an undirected graph with vertices V and edges E. G can be a finite or infinite graph.…”

Section: Introductionmentioning

confidence: 99%

On the Validations of the Asymptotic Matching Conjectures

et al. 2008

View full text Add to dashboard Cite

In this paper we review the asymptotic matching conjectures for rregular bipartite graphs, and their connections in estimating the monomerdimer 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 ∈ [0, 1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.2000 Mathematics Subject Classification: 05A15, 05A16, 05C70, 05C80, 82B20 Keywords and phrases: Matching and asymptotic growth of average matchings for r-regular bipartite graphs, monomer-dimer partitions and entropies.

show abstract

“…See for example [1,2,4,5,6,12,14,15,16,17,19,20,21,23,24,25,26,28,30]. Let G = (V, E) be an undirected graph with vertices V and edges E. G can be a finite or infinite graph.…”

Section: Introductionmentioning

confidence: 99%

On the Validations of the Asymptotic Matching Conjectures

et al. 2008

View full text Add to dashboard Cite

show abstract

“…The middle term is obtained by considering the eigenvalues of A 3,5 , the 10 by 10 matrix whose row and columns are indexed by lexicographically ordered 3-element subsets of [5]. (See [9][10][11].) From the previous section we deduce h(m) = log ρ(m) 2m .…”

Section: The Transfer Matrix Methods For Counting Perfect Matchings Inmentioning

confidence: 99%

Matchings in m-generalized fullerene graphs

2015

Self Cite

View full text Add to dashboard Cite

A connected planar graph is called m-generalized fullerene if two of its faces are mgons and all other faces are pentagons and hexagons. In this paper we first determine some structural properties of m-generalized fullerenes and then use them to obtain new results on the enumerative aspects of perfect matchings in such graphs. We provide both upper and lower bounds on the number of perfect matchings in m-generalized fullerene graphs and state exact results in some special cases.

show abstract

“…Hammersley proved in (19) that the number of p-density configurations on the cube of volume n in d dimensions is of order ȕ(d, p) n for some function ȕ. He spent much effort on obtaining bounds for ȕ, but, even today in two dimensions, our knowledge is very limited (see, for example, Friedland & Peled 2005).…”

Section: Self-avoiding Walks and The Monomer-dimer Problemmentioning

confidence: 99%

John Michael Hammersley. 21 March 1920 — 2 May 2004

Grimmett

Welsh²

2007

Biogr. Mems Fell. R. Soc.

View full text Add to dashboard Cite

John Hammersley was a pioneer among mathematicians, who defied classification as pure or applied; when introduced to guests at Trinity College, Oxford, he would say he did ‘difficult sums’. He believed passionately in the importance of mathematics with strong links to real–life situations and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self–avoiding walks and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem–solver, he was a leader in the movement of the 1950s and 1960s to rethink the content of school mathematics syllabuses.

show abstract

Theory of computation of multidimensional entropy with an application to the monomer–dimer problem

Cited by 37 publications

References 37 publications

On the Validations of the Asymptotic Matching Conjectures

On the Validations of the Asymptotic Matching Conjectures

Matchings in m-generalized fullerene graphs

John Michael Hammersley. 21 March 1920 — 2 May 2004

Contact Info

Product

Resources

About