Article ID Journal Published Year Pages File Type
5772584 Journal of Number Theory 2017 14 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, , ,