Binomial transforms and integer partitions into parts of k different magnitudes
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A relationship between the general linear group of degree n over a finite field and the integer partitions of n into parts of k different magnitudes was investigated recently by the author. In this paper, we use a variation of the classical binomial transform to derive a new connection between partitions into parts of k different magnitudes and another finite classical group, namely the symplectic group Sp. New identities involving the number of partitions of n into parts of k different magnitudes are introduced in this context.
KeywordsBinomial transform Integer partitions Symplectic group
Mathematics Subject Classification05E15 05A19 05A17
The author appreciates the anonymous referees for their comments on the original version of this paper. Special thanks go to Dr. Oana Merca for the careful reading of the manuscript and helpful remarks.
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