From sets to functions: Three elementary examples

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Abstract

A sequence of binomial type is a basis for R[x] satisfying a binomial-like identity, e.g. powers, rising and falling factorials. Given two sequences of binomial type, the authors describe a totally combinatorial way of finding the change of basis matrix: to each pair of sequences is associated a poset whose Whitney numbers of the 1st and 2nd kind give the entries of the matrix and its inverse.

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Research partially supported by NSF Grant MCS77-01947.

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Research partially supported by NSF Grant MCS78-02743.