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Combinatorics of two second-order mock theta functions

School of Mathematics, University of Minnesota, Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA

https://doi.org/10.1142/S1793042120400229Cited by:1 (Source: Crossref)

This article is part of the issue:

Special Issue I: In Honor of Bruce Berndt’s 80th Birthday
Editors: George E. Andrews, Michael Filaseta and Ae Ja Yee

Abstract

We introduce combinatorial interpretations of the coefficients of two second-order mock theta functions. Then, we provide a bijection that relates the two combinatorial interpretations for each function. By studying other special cases of the multivariate identity proved by the bijection, we obtain new combinatorial interpretations for the coefficients of Watson’s third-order mock theta function $ω (q)$ $ω (q)$ and Ramanujan’s third-order mock theta function $f (q)$ $f (q)$ .

Keywords:

AMSC: 05A17, 11P84

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