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Generating functions and combinatorial identities. (English) Zbl 0907.05005

The author establishes an equivalence of the Abel identities and Euler’s binomial theorem, as well as of the Hagen-Rothe identities and Vandermonde’s convolution formula, using the mixed generating function of L. Carlitz for renewal sequences; see L. Carlitz [SIAM J. Math. Anal. 8, No. 3, 518-532 (1977; Zbl 0357.33004)]. As a generalization, he developes two kinds of multifold analogues and their applications to combinatorial identities of multivariate convolutions; see S. G. Mohanty and B. R. Handa [Can. Math. Bull. 12, 45-74 (1969; Zbl 0193.36603)].
Reviewer: I.Strazdins (Riga)

MSC:

05A15 Exact enumeration problems, generating functions
05A19 Combinatorial identities, bijective combinatorics
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