3 papers
math.CO2026
The Gröbner Version of White's Conjecture is False
Spencer Backman, Nathan Cheung, MichaÅ LasoÅ +2
We show that the toric ideal of the Fano matroid polytope does not have a quadratic Gröbner basis. This resolves in the negative a strong version of White's conjecture from matroi…
math.AG2025
The geometric Merkurjev-Panin Conjecture for the Cox category
Daniel Erman, Andrew Hanlon, Gaku Liu +1
We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exception…
math.AG2025
Mixed Eulerian numbers and beyond
Gaku Liu, Mateusz MichaÅek, Julian Weigert
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…