A new combinatoric estimate for cluster expansions
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We state and prove a new and previously unsuspected tree graph inequality, which is significantly stronger than the one commonly applied to cluster expansions. The older inequality controls the counting problem in the convergence proof of such an expansion, but the new inequality does more: it also exhibits extra 1/n! factors that can be applied to the cancellation of number divergences. The proof of this new combinatoric estimate is completely elementary. © 1984 Springer-Verlag.
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