The Ramanujan Journal

, Volume 48, Issue 2, pp 305–322 | Cite as

On certain weighted 7-colored partitions

  • Shane Chern
  • Dazhao TangEmail author


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.


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

Mathematics Subject Classification

05A17 11P83 05A30 



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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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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