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ON THE SUM OF PARTS IN THE PARTITIONS OF n INTO DISTINCT PARTS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  11 December 2020

MIRCEA MERCA Open the ORCID record for MIRCEA MERCA [Opens in a new window]
MIRCEA MERCA*
Affiliation:
Department of Mathematics, University of Craiova, 200585Craiova, Romania
*
e-mail: mircea.merca@profinfo.edu.ro
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Abstract

We investigate the sum of the parts in all the partitions of n into distinct parts and give two infinite families of linear inequalities involving this sum. The results can be seen as new connections between partitions and divisors.

Keywords

divisorspartitionstheta series

MSC classification

Primary: 11P81: Elementary theory of partitions
Secondary: 05A19: Combinatorial identities, bijective combinatorics 05A20: Combinatorial inequalities 11P82: Analytic theory of partitions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 228 - 237
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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