A Combinatorial Approach Towards Ramanujan's Partition Congruences Modulo 5, 7 and 11 In Terms Of Its Corresponding Cranks

Abstract The primary purpose of this article is to provide an explicit interpretation of Ramanujan's Partition Congruences, namely, p (5n+4) 0 (mod 5), p (7n+5) 0 (mod 7) and, p (11n+6) 0 (mod 11), p (n) being the partition function corresponding to any positive integer n, in terms of their corresponding Cranks using various combinatorial arguments implemented by Dyson, Atkin, Swinnerton-Dyer and later by Andrews and, Garvan to justify all the necessary concepts pertaining to this topic. 2020 MSC: Primary 11-02, 11P81, 11P82, 11P83, 11P84. Secondary 11B75, 05A16, 05A17, 05A30.