3 papers
math.CO2026
The mapping index through the lens of the cross-index
Vuong Bui, Hamid Reza Daneshpajouh, Roman Karasev
We study the cross-index of free \(G\)-posets as a combinatorial analogue of the equivariant topological index. We demonstrate that the cross-index exhibits many structural propert…
math.MG2026
Rogers's proof of Vaaler's theorem
Roman Karasev
We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.
math.GT2025
Short proofs of Tverberg-type theorems for cell complexes
Roman Karasev, Arkadiy Skopenkov
We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power , any comp…