Sabuj Das

On Partition Theory Sabuj Das

A partition of n is a division of n into any number of positive integral parts. Then the sum of the integral parts is n. The order of the parts and arrangement in a division of n are irrelevant and the parts are arranged in descending order. We denote the number of partitions of n by P(n). We introduce a brief survey of Ramanujan?s partitions congruences. We mainly concern with combinatorial aspects of the congruences moduli 5, 7 in terms of the rank and crank of vector partitions separately.