\(1/n\) expansion for the number of matchings on regular graphs and Monomer-Dimer entropy

DOI10.1007/s10955-017-1819-6zbMath1376.82022OpenAlexW2620185270MaRDI QIDQ2410494

Mario Pernici

Publication date: 18 October 2017

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-017-1819-6

zbMATH Keywords

latticeentropymatchingregular graphrandom graphDimer

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Statistical mechanics of polymers (82D60) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (1)

A mysterious cluster expansion associated to the expectation value of the permanent of \(0\)-\(1\) matrices

Uses Software

• SageMath

Cites Work

• Unnamed Item
• An asymptotic expansion and recursive inequalities for the monomer-dimer problem
• On the number of matchings in regular graphs
• The number of matchings in random regular graphs and bipartite graphs
• A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
• The expected eigenvalue distribution of a large regular graph
• A positivity property of the dimer entropy of graphs
• A mysterious cluster expansion associated to the expectation value of the permanent of \(0\)-\(1\) matrices
• Theory of monomer-dimer systems
• The statistics of dimers on a lattice
• Counting Matchings and Tree-Like Walks in Regular Graphs
• Statistical Mechanics of Dimers on a Plane Lattice
• The number of matchings in random graphs
• Asymptotic enumeration of Latin rectangles

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