Colored partition identities conjectured by Sandon and Zanello

Recently, Sandon and Zanello (Ramanujan J 33: 83–120, 2014 ) conjectured 29 highly non-trivial colored partition identities. In this paper, we establish 17 of them and prove analogous colored partition identities of the remaining 12 conjectural identities by using the theory of Ramanujan’s theta functions. We also present some new colored partition identities of the same type.