Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772584 | Journal of Number Theory | 2017 | 14 Pages |
Abstract
In the first part of this paper we introduce overpartitions into distinct parts without k-sequences. When k=1 these are the partitions into parts differing by at least two which occur in the Rogers-Ramanujan identities. For general k we compute a three-variable double sum q-hypergeometric generating function and give asymptotic estimates for the number of such overpartitions. When k=2 we obtain several more double sum generating functions as well as a combinatorial identity. In the second part of the paper, we establish arithmetic and combinatorial properties of some related q-hypergeometric double sums.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Youn-Seo Choi, Byungchan Kim, Jeremy Lovejoy,