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<p>We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by Berget, Eur, Spink and Tseng to the product space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\mathbb {P}}}^n \times {{\mathbb {P}}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>, we establish an equivariant generalization of the Tutte polynomial of a matroid. We discuss how this polynomial encodes properties of the matroid by looking at special evaluations. We further introduce an equivariant generalization of the reduced characteristic polynomial of a matroid.</p>

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Equivariant Tutte Polynomial

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月23日

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  • Mario Bauer,
  • Matěj Doležálek,
  • Magdaléna Mišinová,
  • Semen Słobodianiuk,
  • Julian Weigert

摘要

We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by Berget, Eur, Spink and Tseng to the product space \({{\mathbb {P}}}^n \times {{\mathbb {P}}}^n\) P n × P n , we establish an equivariant generalization of the Tutte polynomial of a matroid. We discuss how this polynomial encodes properties of the matroid by looking at special evaluations. We further introduce an equivariant generalization of the reduced characteristic polynomial of a matroid.