Arithmetic Properties of Overpartition Pairs

Details Arithmetic Properties of Overpartition Pairs Arithmetic Properties of Overpartition Pairs

2010-09-25

arxiv.org/abs/1009.5016v1

Mathematics

Combinatorics

19 pages

Scientific paper

Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of $\bar{pp}(n)$, the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number $\bar{pp}(n)$. In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for $\bar{pp}(n)$. Moreover, we find three ranks as combinatorial interpretations of the fact that $\bar{pp}(n)$ is divisible by three for any n. We also construct infinite families of congruences for $\bar{pp}(n)$ modulo 3, 5, and 9.

Affiliated with

Also associated with

No associations

Rating

Arithmetic Properties of Overpartition Pairs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Arithmetic Properties of Overpartition Pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetic Properties of Overpartition Pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-696038