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We prove a new convergence condition for the activity expansion of
correlation functions in equilibrium statistical mechanics with possibly
negative pair potentials. For non-negative pair potentials, the criterion is an
if and only if condition. The condition is formulated with a sign-flipped
Kirkwood-Salsburg operator and known conditions such as Koteck\${\’y}\$-Preiss
and Fern\${\’a}\$ndez-Procacci are easily recovered. In addition, we deduce new
sufficient convergence conditions for hard-core systems in \$\mathbb R^d\$ and
\$\mathbb Z^d\$ as well as for abstract polymer systems. The latter improves on
the Fern\${\’a}\$ndez-Procacci criterion.

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