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Sequences of Symmetric Functions of Binomial Type
Author(s) -
loeb Daniel E.
Publication year - 1990
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19908311
Subject(s) - mathematics , binomial coefficient , binomial (polynomial) , gaussian binomial coefficient , sequence (biology) , type (biology) , binomial theorem , binomial approximation , operator (biology) , negative binomial distribution , binomial distribution , context (archaeology) , symmetric function , identity (music) , combinatorics , generating function , central binomial coefficient , discrete mathematics , pure mathematics , statistics , poisson distribution , physics , biology , ecology , paleontology , biochemistry , chemistry , repressor , gene , transcription factor , acoustics , genetics
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 umbra! 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.