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

Download Citation

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

Keywords: partition congruences , partition identities , regular bipartition , Theta-functions

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

Vol.12 • No. 3 • July 2019
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