TY - JOUR
T1 - On the sum of parts with multiplicity at least 2 in all the partitions of n
AU - Merca, Mircea
AU - Yee, Ae Ja
N1 - Funding Information:
The authors would like to thank the anonymous referee for his/her valuable comments. The second author was partially supported by a grant (#633963) from the Simons Foundation.
Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/4
Y1 - 2021/4
N2 - 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.
AB - 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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U2 - 10.1142/S1793042120400205
DO - 10.1142/S1793042120400205
M3 - Article
AN - SCOPUS:85093984828
SN - 1793-0421
VL - 17
SP - 665
EP - 681
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 3
ER -