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On Uchimura’s Connection between Partitions and the Number of Divisors

Published online by Cambridge University Press:  20 November 2018

D. M. Bressoud  and
M. V. Subbarao
D. M. Bressoud
Affiliation:
Pennsylvania State UniversityUniversity Park, Pennsylvania16802
M. V. Subbarao
Affiliation:
Pennsylvania State UniversityUniversity Park, Pennsylvania16802
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Abstract

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A combinatorial proof is given for Uchimura’s identity

As a corollary to this proof we derive a formula for the sum of the nth powers of the divisors of m in terms of partitions of m.

Keywords

10A4510A2005A17
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 143 - 145
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Uchimura, K., An identity for the divisor generating function arising from sorting theory, J. Comb Th. (A) 31 (1981), 131–135.Google Scholar
2. Uchimura, K., Identities for divisor generating functions and their relations to a probability generating function, preprint.Google Scholar