
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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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | April 1, 2021 |
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Deposited | July 07, 2021 |
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