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Equivariant Tutte Polynomial
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DOI：10.1007/s00454-025-00773-y.png)
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Abstract
En 中文
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 PnxPn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {P}}}<^>n \times {{\mathbb {P}}}<^>n$$\end{document}, 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.
Keywords:
Matroids
Equivariant cohomology
Permutohedral variety
Potts model
Tutte polynomials
Characteristic polynomials
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