Combinatorics of two second-order mock theta functions

Hannah Burson

doi:10.1142/s1793042120400229

Combinatorics of two second-order mock theta functions

Hannah Burson

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	285-295
Number of pages	11
Journal	International Journal of Number Theory
Volume	17
Issue number	2
DOIs	https://doi.org/10.1142/s1793042120400229
State	Published - Nov 12 2020

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Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

Partitions
mock theta functions
q-series

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10.1142/s1793042120400229

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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).",

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AB - 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).

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KW - q-series

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JF - International Journal of Number Theory

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ER -

Combinatorics of two second-order mock theta functions

Abstract

Bibliographical note

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