We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Generalizations of Dyson's rank on overpartitions.
- Authors
Zhao, Alice X. H.
- Abstract
We introduce a statistic on overpartitions called the k ¯ -rank. When there are no overlined parts, this coincides with the k -rank of a partition introduced by Garvan. Moreover, it reduces to the D-rank of an overpartition when k = 2. The generating function for the k ¯ -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 X(q) and χ (q).
- Subjects
GENERATING functions; THETA functions; GENERALIZATION; PARTITIONS (Mathematics)
- Publication
International Journal of Number Theory, 2022, Vol 18, Issue 4, p743
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042122500397