Some Missed Congruences modulo powers of $2$ for $t$-colored overpartitions

TL;DR

This paper extends known congruences for t-colored overpartitions modulo powers of 2 using an algorithmic approach, building upon recent results for specific values of t.

Contribution

It introduces an algorithmic method to find additional congruences for t-colored overpartitions beyond previously known cases.

Findings

Extended congruences for t-colored overpartitions modulo 16 and 32.

Applied an algorithmic technique to discover new congruences.

Built upon recent results for t=5,7,11,13.

Abstract

Recently, Nayaka and Naika (2022) proved several congruences modulo $16$ and $32$ for $t$-colored overpartitions with $t=5,7,11$ and $13$. We extend their list using an algorithmic technique.