English

Partition Identities for Ramanujan's Third Order Mock Theta Functions

Combinatorics 2010-06-17 v1 Number Theory

Abstract

We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions ϕ(q)\phi(-q) and ψ(q)\psi(-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.

Keywords

Cite

@article{arxiv.1006.3194,
  title  = {Partition Identities for Ramanujan's Third Order Mock Theta Functions},
  author = {William Y. C. Chen and Kathy Q. Ji and Eric H. Liu},
  journal= {arXiv preprint arXiv:1006.3194},
  year   = {2010}
}

Comments

12 pages, 1 figure

R2 v1 2026-06-21T15:37:06.067Z