On some relations for the rank moduli 9 and 12

AbstractIn this paper we prove some identities, conjectured by Lewis, concerning the rank moduli 9 and 12, which are similar to Dyson's identities for the rank moduli 5 and 7 which give a combinatorial explanation to Ramanujan's partition congruences. For this we use multisection of series and some identities for the third and sixth order Mock theta functions, in such a way that all the identities for a given modulus reduce to a single theta identity