Abstract
We introduce the partition polynomial of a finite set system, which generalizes the matching polynomial of a graph, and elucidate some of its properties. Among these are its connections with the matching polynomial and with a generalized chromatic polynomial and various structural conditions which imply that the partition polynomial has only real roots. The properties of the partition polynomial with respect to composition of set systems also prove interesting; the main result is an extension of the Heilmann-Lieb Theorem to this context.
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