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Contravariant Functors on Finite Sets and Stirling Numbers

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Robert Paré

We characterize the numerical functions which arise as the
cardinalities of contravariant functors on finite sets, as those which have
a series expansion in terms of Stirling functions. We give a procedure for
calculating the coefficients in such series and a concrete test for
determining whether a function is of this type. A number of examples are
considered.

Keywords: Functor, cardinality, Stirling numbers.

1991 MSC: 18A22, 05A10.

*Theory and Applications of Categories*, Vol. 6, 1999, No. 5, pp 65-76.

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