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Combinatorics and cluster expansions
2010
Probability Surveys
This article is about the connection between enumerative combinatorics and equilibrium statistical mechanics. The combinatorics side concerns species of combinatorial structures and the associated exponential generating functions. The passage from species to generating functions is a combinatorial analog of the Fourier transform. Indeed, there is a convolution multiplication on species that is mapped to a pointwise multiplication of the exponential generating functions. The statistical
doi:10.1214/10-ps159
fatcat:f2yqv7dxjbcepjk3siceiv6lxa