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The Ramanujan Journal

, Volume 46, Issue 3, pp 765–774 | Cite as

Binomial transforms and integer partitions into parts of k different magnitudes

  • Mircea Merca
Article

Abstract

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.

Keywords

Binomial transform Integer partitions Symplectic group 

Mathematics Subject Classification

05E15 05A19 05A17 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Academy of Romanian ScientistsBucharestRomania

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