On certain weighted 7-colored partitions

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Abstract

Inspired by Andrews’ 2-colored generalized Frobenius partitions, we consider certain weighted 7-colored partition functions and establish some interesting Ramanujan-type identities and congruences. Moreover, we provide combinatorial interpretations of some congruences modulo 5 and 7. Finally, we study the properties of weighted 7-colored partitions weighted by the parity of certain partition statistics.

Keywords

Weighted 7-colored partition Ramanujan-type congruence Unified multirank Vector crank 

Mathematics Subject Classification

05A17 11P83 05A30 

Notes

Acknowledgements

The authors would like to thank George E. Andrews, Shishuo Fu, Michael D. Hirschhorn, and Ae Ja Yee for their helpful comments and suggestions that have improved this paper to a great extent. The authors also acknowledge the helpful suggestions made by the referee.

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

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityState CollegeUSA
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China

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