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<p>We define a two-parameter deformation of the quasi-shuffle by means of the formal group law associated with the exponential generating function of the homogeneous Eulerian polynomials, and construct bases of <i>QSym</i> and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{WQSym}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">WQSym</mi> </math></EquationSource> </InlineEquation> whose product rule is given by this operation.</p>

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A two-parameter deformation of the quasi-shuffle and new bases of quasi-symmetric functions

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Olivier Bouillot,
  • Jean-Christophe Novelli,
  • Jean-Yves Thibon

摘要

We define a two-parameter deformation of the quasi-shuffle by means of the formal group law associated with the exponential generating function of the homogeneous Eulerian polynomials, and construct bases of QSym and \(\textbf{WQSym}\) WQSym whose product rule is given by this operation.