On Ramanujan-type Congruences for Partition Triples and Quadruples with 7-Cores

Veeresha R G; Akshay H K

doi:10.5269/bspm.79410

On Ramanujan-type Congruences for Partition Triples and Quadruples with 7-Cores

Veeresha R G Department of Mathematics, Sri Jayachamarajendra College of Engineering, JSS Science and Technology University, Manasagangotri, Mysuru-570006, Karnataka https://orcid.org/0000-0003-1297-0568
Akshay H K Department of Mathematics, Sri Jayachamarajendra College of Engineering, JSS Science and Technology University, Mysuru https://orcid.org/0009-0009-0803-9990

Abstract

Let $B_t(k)$ and $C_t(k)$ denote the number of partitons of $3$ and $4$-tuples of $k$ with $7$-core partition respectively. In this article we establish some Ramanujan-type congruences modulo $3$ for $B_t(k)$ and modulo $2$ for $C_t(k)$.