Partition Identities for Ramanujan's Third Order Mock Theta Functions
William Y. C. Chen, Kathy Q. Ji, and Eric H. Liu
Abstract: We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on the mock theta function f(q). The two classical identities of Ramanujan on third order mock theta functions are consequences of these partition identities. Our combinatorial constructions also apply to Andrews' generalizations of Ramanujan's identities. AMS Classification: 05A17, 11P81 Keywords: mock theta function, Ramanujan's identities, partition identity, Fine's theorem, involution Download: PDF |