Arithmetic properties of $t$-Schur overpartitions

TL;DR

This paper investigates the arithmetic properties of $t$-Schur overpartitions, a generalization of classical partitions, focusing on specific cases where $t=3,9$ or powers of 2 and 3, revealing new number-theoretic insights.

Contribution

It extends the study of $t$-Schur overpartitions by proving new arithmetic results for particular values of $t$, including powers of 2 and 3.

Findings

Arithmetic properties established for $t=3,9$

Results for $t$ as powers of 2 or 3

Generalization of classical Schur partitions

Abstract

In a recent work, Nadji and Ahmia introduced the $t$-Schur overpartitions as an overpartition analogue for $t$-Schur partitions, which generalizes the classical Schur's partitions into parts congruent to $1$ or $5$ modulo $6$. We continue the study of this new class of overpartitions and prove several arithmetic results for the cases $t=3,9$ and $t$ being a power of $2$ or a power of $3$.