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<p>Recently, Nadji and Ahmia introduced the notion of <i>t</i>-Schur overpartitions and investigated their combinatorial and arithmetic properties. In this paper, we extend their work and establish several new congruence relations for <i>t</i>-Schur overpartitions. For example, for all <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n \ge 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> we prove <Equation ID="Equ178"> <EquationSource Format="TEX">\( \overline{S_9}(24n+23) \equiv 0 \pmod {32}. \)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mover> <msub> <mi>S</mi> <mn>9</mn> </msub> <mo>¯</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mn>24</mn> <mi>n</mi> <mo>+</mo> <mn>23</mn> <mo stretchy="false">)</mo> </mrow> <mo>≡</mo> <mn>0</mn> <mspace width="10.0pt" /> <mrow> <mo stretchy="false">(</mo> <mo>mod</mo> <mspace width="0.277778em" /> <mn>32</mn> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mrow> </math></EquationSource> </Equation></p>

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Extending recent congruence results on \(t-\)Schur overpartitions

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • K. C. Ajeyakashi,
  • H. S. Sumanth Bharadwaj,
  • S. Chandankumar

摘要

Recently, Nadji and Ahmia 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 \(n \ge 0\) n ≥ 0 we prove \( \overline{S_9}(24n+23) \equiv 0 \pmod {32}. \) S 9 ¯ ( 24 n + 23 ) ≡ 0 ( mod 32 ) .