# CSM

## Seminar

### An introduction to the Mayer expansion

Seminar Room 1, Newton Institute

#### Abstract

I define the repulsive lattice gas on a vertex set X (which includes the independent-set polynomial of a graph G as a special case) and briefly explain its relevance in statistical physics and in combinatorics. I then describe the Mayer expansion for the logarithm of the lattice-gas partition function, and analyze some of its combinatorial properties. Next, I describe two approaches to proving the convergence of the Mayer expansion in a complex polydisc: the traditional graphical approach and Dobrushin's inductive approach. Finally, I explain briefly the surprising connection between the independent-set polynomial and the Lovasz local lemma in probabilistic combinatorics.

**Related Links**

- http://arxiv.org/abs/cond-mat/0309352 - The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma (by Alex Scott and myself)

#### Video

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