2025/02/07 by Liu, Gaku, Michałek, Mateusz, Weigert, Julian
#05E14 #14C17 #14N15 #52A39 #52B40 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.04980
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 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.