Helly theorem for affine spaces without dimensions
Combinatorics
2025-12-01 v2 Computational Geometry
Abstract
We prove a no-dimensional Helly theorem for affine spaces and convex sets using the unboundedness framework of Aronov, Goodman, and Pollack (Computational Geometry, 2002). This generalizes the fundamental result of Adiprasito, B\'ar\'any, Mustafa, and Terpai on the no-dimensional Helly theorem for points and convex sets (Discrete & Computational Geometry, 2020). Additionally, we establish the optimality of our result.
Cite
@article{arxiv.2308.10480,
title = {Helly theorem for affine spaces without dimensions},
author = {Sutanoya Chakraborty and Arijit Ghosh and Soumi Nandi},
journal= {arXiv preprint arXiv:2308.10480},
year = {2025}
}
Comments
Updated title and abstract; rewrote proofs in Section 3. Now 10 pages with 2 figures