Combinatorics of two second-order mock theta functions

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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) and Ramanujan's third-order mock theta function f(q).

Original languageEnglish (US)
Pages (from-to)285-295
Number of pages11
JournalInternational Journal of Number Theory
Volume17
Issue number2
DOIs
StatePublished - Mar 2021

Bibliographical note

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

  • Partitions
  • mock theta functions
  • q-series

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