Further Arithmetic Properties of Overcubic Partition Triples

TL;DR

This paper establishes new congruences for overcubic partition triples using elementary and modular form techniques, extends the concept to overcubic partition k-tuples, and explores their arithmetic properties.

Contribution

It introduces new congruences for overcubic partition triples and generalizes the concept to overcubic partition k-tuples with related arithmetic properties.

Findings

New congruences for overcubic partition triples

Generalization to overcubic partition k-tuples

Arithmetic properties of the generalized partitions

Abstract

In this short note, we prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka, Dharmendra, and Kumar (2024). We also generalize overcubic partition triples to overcubic partition $k$-tuples and prove a few arithmetic properties for these type of partitions.