An upper bound for the multidimensional dimer problem

Author:

Minc Henryk

Abstract

AbstractA recently proved upper bound for the permanents of (0,1) matrices is used to improve the Fowler-Rushbrooke upper bound for the constant λd occurring in the d-dimensional dimer problem, d ≥ 3.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices

2. Existence theorems and Monte Carlo methods for the monomer-dimer problem;Hammersley;Research papers in statistics: Festschrift for J. Neyman,1966

3. An attempt to extend the statistical theory of perfect solutions

4. An improved lower bound for the multidimensional dimer problem

5. Certain properties of nonnegative matrices and their permanents;Brégman;Dokl. Akad. Nauk SSSR,1973

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1. Dimer problem for some three dimensional lattice graphs;Physica A: Statistical Mechanics and its Applications;2016-02

2. Henryk Minc - A Biography;Linear and Multilinear Algebra;2003-01

3. Approximating the Permanent via Importance Sampling with Application to the Dimer Covering Problem;Journal of Computational Physics;1999-02

4. An improved upper bound for the 3 -dimensional dimer problem;Duke Mathematical Journal;1998-07-15

5. Van der Waerden Conjecture and Applications;Handbook of Algebra;1996

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