Extending Recent Arithmetic Properties of Overcubic Partition Tuples

Abstract

In recent years, several mathematicians have looked at a class of partitions called the overcubic partition $k$-tuples, for small values of $k$. They have proved several divisibility results satisfied by these partitions. We continue this study and prove a few infinite family of congruences. Our proofs use elementary techniques from $q$-series and number theory.