We establish several identities for partitions with distinct colors that arise from Ramanujan’s formulas for multipliers in the theory of modular equations. In the course of our investigations, we prove three conjectures made by C. Sandon and F. Zanello. However, combinatorial proofs of these three conjectures and most of the theorems in this paper remain to be given.
- colored partitions
- modular equations
- theta function identities
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics