3 papers
math.CO2026
The affine Tverberg theorem revisited
Sergey Avvakumov, Roman Karasev
We prove the Bárány--Kalai--Tverberg conjecture extending the affine version of Tverberg's theorem to simplicial balls and polytopes other than the simplex: For any affine map $ϕ:…
math.CO2026
Cone and constrained colorful Carathéodory Theorems
Pavle V. M. Blagojević, Roman N. Karasev, Bálint Zsigri
Holmsen proved in 2016 a generalization of the classical colorful Caratheodory theorem in which a matroid imposes additional constraints on the desired colorful transversal. His ap…
math.CO2025
Tensor rank of the determinant and periodic triangulations of
Sergey Avvakumov, Roman Karasev
We prove that in any -periodic triangulation of the number of -orbits of -dimensional simplices is at least the tensor rank of the …