Mixed Eulerian numbers and beyond
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909482968154112 |
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| author | Liu, Gaku Michałek, Mateusz Weigert, Julian |
| author_facet | Liu, Gaku Michałek, Mateusz Weigert, Julian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed Eulerian numbers and beyond Liu, Gaku Michałek, Mateusz Weigert, Julian Algebraic Geometry Combinatorics 14C17, 14N15, 52A39, 05E14, 52B40 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. |
| title | Mixed Eulerian numbers and beyond |
| topic | Algebraic Geometry Combinatorics 14C17, 14N15, 52A39, 05E14, 52B40 |
| url | https://arxiv.org/abs/2502.04980 |