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<p>We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine <i>n</i>-space. Our results give graded and representation-theoretic enhancements of the sequence of numbers <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c_n=1 + (n-2)\cdot 2^{n-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mo>·</mo> <msup> <mn>2</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, sequence 337 of the Online Encyclopaedia of Integer Sequences, involving a symmetric version of the Bernoulli triangle.</p>

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Ideals, representations and a symmetrised Bernoulli triangle

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月6日

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  • Nsibiet E. Udo,
  • Praise Adeyemo,
  • Balázs Szendrői,
  • Stavros Argyrios Papadakis

摘要

We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine n-space. Our results give graded and representation-theoretic enhancements of the sequence of numbers \(c_n=1 + (n-2)\cdot 2^{n-1}\) c n = 1 + ( n - 2 ) · 2 n - 1 , sequence 337 of the Online Encyclopaedia of Integer Sequences, involving a symmetric version of the Bernoulli triangle.