Generalizations of Dyson’s rank on overpartitions

Author:

Zhao Alice X. H.1

Affiliation:

1. College of Science, Tianjin University of Technology, Tianjin 300384, P. R. China

Abstract

We introduce a statistic on overpartitions called the [Formula: see text]-rank. When there are no overlined parts, this coincides with the [Formula: see text]-rank of a partition introduced by Garvan. Moreover, it reduces to the D-rank of an overpartition when [Formula: see text]. The generating function for the [Formula: see text]-rank of overpartitions is given. We also establish a relation between the generating function of self-3-conjugate overpartitions and the tenth-order mock theta functions [Formula: see text] and [Formula: see text].

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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