Computing the partition function for graph homomorphisms with multiplicities

Alexander Barvinok, Pablo Soberón

Introduction and main results

(1.1) Partition function of graph homomorphisms with prescribed multiplicities

(1.2) Independent sets in graphs

(1.3) Hafnians, Hamiltonian permanents, and subgraph densities

(1.4) Graph colorings

(1.5) Partition function of edge-colored graph homomorphisms with multiplicities

(1.6) Partition functions in combinatorics

The algorithm

(2.1) The algorithm

Recurrence relations

(3.1) Definitions

(3.2) Recurrence relations

Angles in the complex plane

Derivatives

Proof of Theorem 2.3

Acknowledgments

References