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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Studies in Applied Mathematics
( Vol. 83 NO.1 / (1990))
Sequences of Symmetric Functions of Binomial Type
Daniel E. Loeb,
Pages. 1-30
Abstract We take advantage of the combinatorial interpretations of many sequences of polynomials of binomial type to define a sequence of symmetric functions corresponding to each sequence of polynomials of binomial type. We derive many of the results of umbral calculus in this context, including a Taylor expansion and a binomial identity for symmetric functions. Surprisingly, the delta operators for all the sequences of binomial type correspond to the same operator on symmetric functions.
Contents 1. Introduction
2. Combinatorial interpretations
3. Symmetric functions
4. Generating functions
5. The symmetric derivative
6. The iterated symmetric derivative
7. The binomial theorem
8. Shift-invariant operators
9. Coalgebras
Key words
Mathmatical Subject Classification