Combinatorica
Lopsided Lova´sz Local Lemma and Latin transversals
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
New versions of Suen's correlation inequality
proceedings of the eighth international conference on Random structures and algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
Combinatorics, Probability and Computing
The bivariate Ising polynomial of a graph
Discrete Applied Mathematics
The independence polynomial of rooted products of graphs
Discrete Applied Mathematics
Proceedings of the forty-third annual ACM symposium on Theory of computing
An improvement of the lovász local lemma via cluster expansion
Combinatorics, Probability and Computing
Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs
Journal of Combinatorial Theory Series B
The lefthanded local lemma characterizes chordal dependency graphs
Random Structures & Algorithms
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We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovász Local Lemma in probabilistic combinatorics. We show that the conclusion of the Lovász Local Lemma holds for dependency graph $G$ and probabilities $\{p_x\}$ if and only if the independent-set polynomial for $G$ is nonvanishing in the polydisc of radii $\{p_x\}$. Furthermore, we show that the usual proof of the Lovász Local Lemma – which provides a sufficient condition for this to occur – corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer [28] and explicitly by Dobrushin [12, 13]. We also present a generalization of the Lovász Local Lemma that allows for ‘soft’ dependencies. The paper aims to provide an accessible discussion of these results, which are drawn from a longer paper [26] that has appeared elsewhere.