Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities

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Authors

  • S. Sharma
     Department of Mathematics, Yadavindra College of Engineering, Punjabi University, Guru Kashi Campus, Talwandi Sabo ,IN
  • M. Rana
     School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004 ,IN

DOI:

https://doi.org/10.18311/jims/2022/29312

Keywords:

Partitions, n–color partitions, mock theta functions, Rogers–Ramanujan identities

Abstract

Combinatorial interpretations of the Rogers–Ramanujan identities are provided in terms of n–color partitions. Further interpretations in terms of ordinary partitions are obtained by using bijective maps. These results lead to the interpretations of two fifth order mock theta functions by attaching weights.

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Published

2022-01-27

How to Cite

Sharma, S., & Rana, M. (2022). Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities. The Journal of the Indian Mathematical Society, 89(1-2), 167–171. https://doi.org/10.18311/jims/2022/29312

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

License

Copyright (c) 2022 S. Sharma, M. Rana

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

References

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S. Sharma and M. Rana, Combinatorial interpretations of mock theta functions by attaching weights, Discrete Math., 341(7) (2018), 1903–1914. DOI: https://doi.org/10.1016/j.disc.2018.03.017

S. Sharma and M. Rana, On mock theta functions and weight-attached Frobenius partitions, Ramanujan J., 50 (2019), 289–303. DOI: https://doi.org/10.1007/s11139-018-0054-3