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 and . 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.
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