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k-Run Overpartitions and Mock Theta Functions
- Publication Year :
- 2012
-
Abstract
- In this paper we introduce k-run overpartitions as natural analogs to partitions without k-sequences, which were first defined and studied by Holroyd, Liggett, and Romik. Following their work as well as that of Andrews, we prove a number of results for k-run overpartitions, beginning with a double summation q-hypergeometric series representation for the generating functions. In the special case of 1-run overpartitions we further relate the generating function to one of Ramanujan's mock theta functions. Finally, we describe the relationship between k-run overpartitions and certain sequences of random events, and use probabilistic estimates in order to determine the asymptotic growth behavior of the number of k-run overpartitions of size n.<br />Comment: 11 pages, 1 figure
- Subjects :
- Mathematics - Number Theory
11P81, 11P82, 05A17, 41A60
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1203.6344
- Document Type :
- Working Paper