- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Congruences modulo 9 for bipartitions with designated summands
Congruences modulo 9 for bipartitions with designated summands
Authors : Robert Xiaojian Hao, Erin Yiying Shen
Pages : 2325-2335
View : 6 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of $n$ is an ordered pair of partitions $(\pi_1, \pi_2)$ with the sum of all of the parts being $n$. In this paper, we investigate arithmetic properties of bipartitions with designated summands. Let $PD_{-2}(n)$ denote the number of bipartitions of $n$ with designated summands. We establish several Ramanujan-like congruences and an infinite family of congruences modulo $9$ satisfied by $PD_{-2}(n)$.Keywords : Partition with designated summands, bipartition, congruence