Scholarlink

<p>We define the notion of <i>k</i>-almost consecutive partitions, and study associated combinatorial and modular aspects. We establish quantum Jacobi properties of their corresponding two-variable partition generating functions. Further, we provide related asymptotics, formulas, and combinatorial identities, and make connections to Ramanujan’s third order mock-theta function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\psi (q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and Cohen’s <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma ^*(q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>σ</mi> <mo>∗</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We conclude by recording a proof of a related conjecture of Xiong.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

k-Almost consecutive partitions and quantum Jacobi forms

  • 期刊论文

  • 发表日期：

    2026年3月11日

查看全文
  • Amanda Folsom,
  • John Joire,
  • Torin Steciuk,
  • Alexandre van Lidth

摘要

We define the notion of k-almost consecutive partitions, and study associated combinatorial and modular aspects. We establish quantum Jacobi properties of their corresponding two-variable partition generating functions. Further, we provide related asymptotics, formulas, and combinatorial identities, and make connections to Ramanujan’s third order mock-theta function \(\psi (q)\) ψ ( q ) and Cohen’s \(\sigma ^*(q)\) σ ∗ ( q ) . We conclude by recording a proof of a related conjecture of Xiong.