On certain weighted 7-colored partitions
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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.
KeywordsWeighted 7-colored partition Ramanujan-type congruence Unified multirank Vector crank
Mathematics Subject Classification05A17 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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