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arXiv · 2312.00913

Equivariant Tutte Polynomial

Mario Bauer·Matěj Doležálek·Magdaléna Mišinová·Semen Słobodianiuk·Julian Weigert
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Abstract

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 A. Berget, C. Eur, H. Spink and D. Tseng to the product space $\mathbb{P}^n \times \mathbb{P}^n$, we establish an equivariant generalization of the Tutte polynomial of a matroid. This was suggested in a survey paper by M.Micha{\l}ek. 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.

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Mario Bauer, Matěj Doležálek, Magdaléna Mišinová, Semen Słobodianiuk, Julian Weigert. 2023-12-01. Equivariant Tutte Polynomial. https://doi.org/10.1007/s00454-025-00773-y

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