83 citations · 542 across the 80 of their papers we have counts for
18 papers · 1 filter
Systolic inequalities and chromatic number
Alexander Kamal, Roman Karasev
We show that the discrete versions of the systolic inequality that estimate the number of vertices of a simplicial complex from below have substantial applications to graphs, the o…
A subexponential size triangulation of
Karim Adiprasito, Sergey Avvakumov, Roman Karasev
We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a tr…
Huang's theorem and the exterior algebra
Roman Karasev
In this note we give a version of Hao Huang's proof of the sensitivity conjecture, shedding some light on the origin of the magical matrix in that proof. For the history of the…
Hedetniemi's conjecture from the topological viewpoint
Hamid Reza Daneshpajouh, Roman Karasev, Alexey Yu. Volovikov
This paper is devoted to studying a topological version of the famous Hedetniemi conjecture which says: The -index of the Cartesian product of two -spaces…
Colorful theorems for strong convexity
Andreas F. Holmsen, Roman Karasev
We prove two colorful Carathéodory theorems for strongly convex hulls, generalizing the colorful Caratéodory theorem for ordinary convexity by Imre Bárány, the non-colorful Carathé…
Residues and the Combinatorial Nullstellensatz
Roman Karasev
We interpret the Combinatorial Nullstellensatz of Noga Alon as a multidimensional residue formula, describe some consequences of this interpretation and related open problems.