On the sum of parts with multiplicity at least 2 in all the partitions of n

Mircea Merca, Ae Ja Yee

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate the sum of distinct parts that appear at least 2 times in all the partitions of n providing new combinatorial interpretations for this sum. A connection with subsets of {1, 2,⋯,n} is given in this context. We provide two different proofs of our results: analytic and combinatorial. In addition, considering the multiplicity of parts in a partition, we provide a combinatorial proof of the truncated pentagonal number theorem of Andrews and Merca.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalInternational Journal of Number Theory
DOIs
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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