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arXiv · 2502.04980

Mixed Eulerian numbers and beyond

Gaku Liu·Mateusz Michałek·Julian Weigert
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Abstract

We derive explicit formulas for the matroidal mixed Eulerian numbers. We resolve a question posed by Berget, Spink, and Tseng, demonstrating that the invariant defined by matroidal mixed Eulerian numbers is precisely equivalent to Derksen's $\mathcal{G}$-invariant. As an application, we provide the first explicit, non-recursive formula for mixed Eulerian numbers. Our combinatorial approach draws inspiration from the classical work of Schubert and incorporates the cutting-edge contributions of Huh.

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Gaku Liu, Mateusz Michałek, Julian Weigert. 2025-02-07. Mixed Eulerian numbers and beyond. https://arxiv.org/abs/2502.04980

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