Title: On certain weighted 7-colored partitions,
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.