Andrews, Lewis and Lovejoy introduced a new class of partitions, partitions with designated summands. Let PD(n) denote the number of partitions of n with designated summands and PDO(n) denote the number of partitions of n with designated summands in which all parts are odd. Andrews et al. established many congruences modulo 3 for PDO(n) by using the theory of modular forms. Baruah and Ojah obtained numerous congruences modulo 3, 4, 8 and 16 for PDO(n) by using theta function identities. In this

more »

... paper, we prove several infinite families of congruences modulo 9, 16 and 32 for PDO(n).