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July 2019 On $(4, 5)$-regular bipartitions with odd parts distinct
M. S. Mahadeva Naika, T. Harishkumar
Tbilisi Math. J. 12(3): 191-208 (July 2019). DOI: 10.32513/tbilisi/1569463243

Abstract

In his work, K. Alladi considered the partition function $pod(n)$, the number of partitions of an integer $n$ with odd parts distinct (the even parts are unrestricted). He obtained a series expansion for the product generating function of these partitions. Later Hirschhorn and Sellers obtained some internal congruences involving the infinite families and Ramanujan's type congruences for $pod(n)$. Let $B_{4, 5}(n)$ denote the number of $(4, 5)$-regular bipartitions of a positive integer $n$ with odd parts distinct. In this paper, we establish many infinite families of congruences modulo powers of $2$ for $B_{4, 5}(n)$.

Funding Statement

The second author would like thank the Ministry of Tribal Affairs, Govt. of India for providing financial assistance under 201718-NFST-KAR-00136 dated 07.06.2018.

Acknowledgment

The authors are thankful to the referee for his comments which improves the quality of our paper.

Citation

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M. S. Mahadeva Naika. T. Harishkumar. "On $(4, 5)$-regular bipartitions with odd parts distinct." Tbilisi Math. J. 12 (3) 191 - 208, July 2019. https://doi.org/10.32513/tbilisi/1569463243

Information

Received: 15 November 2018; Accepted: 20 August 2019; Published: July 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07172334
MathSciNet: MR4012392
Digital Object Identifier: 10.32513/tbilisi/1569463243

Subjects:
Primary: 11P83
Secondary: 05A17

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 3 • July 2019
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