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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A $ q$-analog of restricted growth functions, Dobinski's equality, and Charlier polynomials


Author: Stephen C. Milne
Journal: Trans. Amer. Math. Soc. 245 (1978), 89-118
MSC: Primary 05A15; Secondary 33A65
DOI: https://doi.org/10.1090/S0002-9947-1978-0511401-8
MathSciNet review: 511401
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Abstract: We apply finite operator techniques due to G. C. Rota to a combinatorial identity, which counts a collection of generalized restricted growth functions in two ways, and obtain a q-analog of Charlier polynomials and Dobinski's equality for the number of partitions of an n-set. Our methods afford a unified proof of certain identities in the combinatorics of finite dimensional vector spaces over $ {\text{GF}}(q)$.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0511401-8
Keywords: Restricted growth functions, Dobinski's equality, Charlier polynomials, Eulerian derivative, Eulerian generating function, finite operator calculus, finite field, maximal chain, stabilizer groups of a chain, q-difference operator, q-Stirling numbers of the second kind
Article copyright: © Copyright 1978 American Mathematical Society