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<p>The elementary symmetric partition function is a map on the set of integer partitions. It sends a partition <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. These elementary symmetric partition functions have been studied before, and are related to plethysm. In this note, we study properties of the elementary symmetric partition functions, particularly related to injectivity and the number of parts appearing in their image partitions.</p>

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On partitions associated with elementary symmetric polynomials

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Cristina Ballantine,
  • Shaheen Nazir,
  • Bridget Eileen Tenner,
  • Karlee Westrem,
  • Chenchen Zhao

摘要

The elementary symmetric partition function is a map on the set of integer partitions. It sends a partition \(\lambda \) λ to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of \(\lambda \) λ . These elementary symmetric partition functions have been studied before, and are related to plethysm. In this note, we study properties of the elementary symmetric partition functions, particularly related to injectivity and the number of parts appearing in their image partitions.