Generalizations of Dyson’s rank on overpartitions
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Published:2021-08-28
Issue:
Volume:
Page:1-13
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ISSN:1793-0421
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Container-title:International Journal of Number Theory
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language:en
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Short-container-title:Int. J. Number Theory
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