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The Ramanujan Journal

, Volume 46, Issue 3, pp 713–725 | Cite as

Some inequalities for k-colored partition functions

  • Shane Chern
  • Shishuo Fu
  • Dazhao Tang
Article
  • 118 Downloads

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.

Keywords

Partition Partition inequality Multiplicative property 

Mathematics Subject Classification

05A17 11P83 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China
  3. 3.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China

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