Mixed Eulerian numbers and beyond
Algebraic Geometry
2025-02-10 v1 Combinatorics
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 -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.
Keywords
Cite
@article{arxiv.2502.04980,
title = {Mixed Eulerian numbers and beyond},
author = {Gaku Liu and Mateusz Michałek and Julian Weigert},
journal= {arXiv preprint arXiv:2502.04980},
year = {2025}
}