COMBINATORICS OF THIRD ORDER MOCK THETA FUNCTION $f(q)$ AND SIXTH ORDER MOCK THETA FUNCTIONS $\phi(q), \psi(q)$

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Abstract

The third order mock theta function f(q) is the generating function for the number of partitions with even rank minus the number of partitions with odd rank. In this paper, mock theta function f(q) is interpreted in terms of n–color partitions which lead to a combinatorial proof of the above fact. The two sixth order mock theta functions φ(q) and ψ(q) from Ramanujan’s Lost Notebook are also interpreted in terms of n–color partitions by attaching weights.

Keywords and Phrases

Mock theta functions, (n + t)-color partitions, Generating functions.

A.M.S. subject classification

05A17, 05A19, 11P81.

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