A -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 .

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Additional Information

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