Koustav Banerjee and Prabir Das Adhikary

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 1, Pages 77—87

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## Details

### Authors and affiliations

Koustav Banerjee

*Ramakrishna Mission Vivekananda University
Belur, Howrah 711202, West Bengal, India
*

Prabir Das Adhikary

*Pondicherry University
R. V. Nagar, Kalapet, Puducherry 605014, India
*

### Abstract

In this paper we provide an alterative proof for the congruence modulo 3 of the cubic partition *a*(*n*). That apart we also examine inequalities for *a*(*n*) and provide upper bound for it in the fashion of the classic partition function *p*(*n*).

### Keywords

- Partitions
- Cubic partitions
- Partition congruences

### AMS Classification

- 11P84

### References

- Chan, H.-C. (2010) Ramanujan’s cubic continued fraction and an analog of his most beautiful identity. International Journal of Number Theory, 6.03, 673–680.
- Kruyswijk, D. (1950) On some well-known properties of the partition function
*p*(*n*) and Euler’s infinite product. Nieuw Arch. Wisk, 23, 97–107. - Ahlgren, S. (2000) Distribution of the partition function modulo composite integers
*M*. Mathematische Annalen, 318(4), 795–803. - Chen,W.Y.C, & Lin, B. L. S. (2009) Congruences for the number of cubic partitions derived from modular forms. arXiv preprint arXiv:0910.1263.
- Berndt, B. C. (2006) Number theory in the spirit of Ramanujan (Vol. 34). American Mathematical Society.

## Related papers

## Cite this paper

APABanerjee, K. and Adhikary, P. D. (2017). An elementary alternative proof for Chan’s analogue of Ramanujan’s most beautiful identity and some inequality of the cubic partition. Notes on Number Theory and Discrete Mathematics, 23(1), 77-87.

ChicagoBanerjee, Koustav and Prabir Das Adhikary. “An Elementary Alternative Proof for Chan’s Analogue of Ramanujan’s Most Beautiful Identity and Some Inequality of the Cubic Partition.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 77-87.

MLABanerjee, Koustav and Prabir Das Adhikary. “An Elementary Alternative Proof for Chan’s Analogue of Ramanujan’s Most Beautiful Identity and Some Inequality of the Cubic Partition.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 77-87. Print.