Some new congruences for t-colored overpartition function

Abstract

For any positive integers t and n, let \({\overline{D}}_t(n)\) denote the number of t-colored overpartitions of n, where each part in the partition has t distinct colors. In recent years, several authors established many infinite families of congruences for \({\overline{D}}_t(n)\) by considering different values of t. In this paper, we prove some infinite and particular congruences for the t-colored overpartition function \({\overline{D}}_t(n)\) for \(t = 2; 8m + 2; 8m + 5; 8m + 6; 16m + 2; 16m + 4\,\,\textrm{and}\,\,32m + 4\), where m is any non-negative integer.