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

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.

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Work Title On the sum of parts with multiplicity at least 2 in all the partitions of n
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Open Access
Creators
  1. Mircea Merca
  2. Ae Ja Yee
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. International Journal of Number Theory
Publication Date April 1, 2021
Publisher Identifier (DOI)
  1. https://doi.org/10.1142/S1793042120400205
Deposited July 07, 2021

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