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April 2020 Arithmetic properties of $2$-color overpartition pairs
M. S. Mahadeva Naika, S. Shivaprasada Nayaka
Tbilisi Math. J. 13(2): 67-85 (April 2020). DOI: 10.32513/tbilisi/1593223220

Abstract

Let $\overline{p}_{k, -2}(n)$ counts the number of overpartition pairs of $n$ with 2-color in which one of the colors appears only in parts that are multiples of $k$. We establish several infinite families of congruences modulo powers of $2$ and $3$ for $\overline{p}_{k, -2}(n)$ where $k= 2$ and $3$. For example, for all $n \geq 0$ and $\alpha\geq0$, we have $$\overline{p}_{2, -2}(16\cdot 3^{4\alpha+2}n+34\cdot 3^{4\alpha+1})\equiv 0 \pmod{128},$$ $$\overline{p}_{3, -2}(6\cdot 25^{\alpha+2}n+20\cdot 25^{\alpha+2})\equiv 0 \pmod{27}.$$

Acknowledgment

The authors would like to thank the anonymous referee for helpful comments and suggestions which enhanced the quality of presentation of this paper.

Citation

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M. S. Mahadeva Naika. S. Shivaprasada Nayaka. "Arithmetic properties of $2$-color overpartition pairs." Tbilisi Math. J. 13 (2) 67 - 85, April 2020. https://doi.org/10.32513/tbilisi/1593223220

Information

Received: 9 July 2019; Accepted: 2 January 2020; Published: April 2020
First available in Project Euclid: 27 June 2020

MathSciNet: MR4117807
Digital Object Identifier: 10.32513/tbilisi/1593223220

Subjects:
Primary: 11P81
Secondary: 11P83

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 2 • April 2020
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