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Some inequalities for k-colored partition functions

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A Correction to this article was published on 18 July 2023

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Abstract

Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for k-colored partition functions \(p_{-k}(n)\) for all \(k\ge 2\). This enables us to extend the k-colored partition function multiplicatively to a function on k-colored partitions and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results.

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References

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Acknowledgements

We are indebted to the anonymous referee whose helpful suggestions and comments have made the first section more complete.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Shane Chern

  2. College of Mathematics and Statistics, Chongqing University, Huxi Campus LD506, Chongqing, 401331, People’s Republic of China

    Shishuo Fu

  3. College of Mathematics and Statistics, Chongqing University, Huxi Campus LD206, Chongqing, 401331, People’s Republic of China

    Dazhao Tang

Authors
  1. Shane Chern
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  2. Shishuo Fu
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  3. Dazhao Tang
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Corresponding author

Correspondence to Dazhao Tang.

Additional information

The second and third authors were supported by the National Natural Science Foundation of China (No. 11501061).

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Chern, S., Fu, S. & Tang, D. Some inequalities for k-colored partition functions. Ramanujan J 46, 713–725 (2018). https://doi.org/10.1007/s11139-017-9989-z

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  • DOI: https://doi.org/10.1007/s11139-017-9989-z

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