Extending Recent Congruence Results on $t$-Schur overpartitions

TL;DR

This paper extends recent work on $t$-Schur overpartitions by establishing new congruence relations, including a specific modulo 32 congruence for overpartition counts, advancing understanding of their arithmetic properties.

Contribution

The paper introduces new congruence relations for $t$-Schur overpartitions, expanding the known arithmetic properties of these combinatorial objects.

Findings

Proved a congruence: S_9(24n+23) \u2260 0 mod 32.

Extended previous results on $t$-Schur overpartitions.

Established several new arithmetic congruences.

Abstract

Recently, Nadji and Ahmia~\cite{nadji2021} introduced the notion of $t$-Schur overpartitions and investigated their combinatorial and arithmetic properties. In this paper, we extend their work and establish several new congruence relations for $t$-Schur overpartitions. For example, for all $n \ge 0$ we prove \[ \overline{S_9}(24n+23)\equiv 0 \pmod{32}. \]