2-Rowed Plane Overpartitions Modulo 8 and 16

Authors

DOI:

https://doi.org/10.24996/ijs.2022.63.10.27

Keywords:

Partitions, Overpartitions, Plane overpartitions, Congruences, Sum of divisors function

Abstract

 In a recent study, a special type of plane overpartitions known as k-rowed plane overpartitions has been studied. The function  denotes the number of plane overpartitions of n with a number of rows at most k. In this paper, we prove two identities modulo 8 and 16 for  the plane overpartitions with at most two rows. We completely specify the  modulo 8. Our technique is based on expanding each term of the infinite product of the generating function of the  modulus 8 and 16 and in which the proofs of the key results are dominated by an intriguing relationship between the overpartitions and the sum of divisors, which reveals a considerable link among these functions modulo powers of 2.

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Published

2022-10-30

How to Cite

Al-Saedi, A. H. (2022). 2-Rowed Plane Overpartitions Modulo 8 and 16. Iraqi Journal of Science, 63(10), 4410–4416. https://doi.org/10.24996/ijs.2022.63.10.27

Issue

Section

Mathematics