5 papers
Splitting the Matroid Determinant
Clara Briand, Leonie Kayser, Julian Weigert
The principal matroid determinant of a linear space has been introduced in recent work by Matsubara-Heo and Telen. In this paper, we give the compl…
Polar Degrees of Matroids
Clara Briand, Leonie Kayser, Julian Weigert
We show that the polar degrees of the coordinate-wise inverse of a linear subspace are given by the coefficients of a substitution of the reduced charact…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the t…
Mixed Eulerian numbers and beyond
Gaku Liu, Mateusz Michałek, 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…
White's conjecture for matroids and inner projections
Kangjin Han, Mateusz Michałek, Julian Weigert
White's conjecture predicts quadratic generators for the ideal of any matroid base polytope. We prove that White's conjecture for any matroid implies it also for any matroid $M…