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<p>The great mathematician Srinivasa Ramanujan proved that the partition function has beautiful divisibility properties. Recent research has focused on the arithmetic of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1152_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation>-regular partition function, which counts the partitions where no part is divisible by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1152_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation>. In this paper, we establish parity results for the 17-regular partition function.</p>

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New parity results for the 17-regular partition function

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • A. Vanitha,
  • D. Penniston,
  • M. M. Vibha

摘要

The great mathematician Srinivasa Ramanujan proved that the partition function has beautiful divisibility properties. Recent research has focused on the arithmetic of the \(\ell \) ℓ -regular partition function, which counts the partitions where no part is divisible by \(\ell \) ℓ . In this paper, we establish parity results for the 17-regular partition function.