6 papers · 1 filter
Almost covering all the layers of hypercube with multiplicities
Arijit Ghosh, Chandrima Kayal, Soumi Nandi
Given a hypercube in and , the -th layer of denotes the set of a…
Helly theorem for affine spaces without dimensions
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi
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 gen…
A geometric proof of the infinite -theorem for hyperplane piercing
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi
We provide a geometric proof of the -theorem for piercing compact connected sets by hyperplanes. Our argument uses only elementary properties of convex sets and…
Finite k-Transversals of Infinite Families of Fat Convex Sets
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi
We prove an infinite -theorem for piercing fat compact convex sets in $\RR^d$ with -flats. Additionally, we develop a new framework through which infinite -theorem…
About almost covering subsets of the hypercube
Arijit Ghosh, Chandrima Kayal, Soumi Nandi
Let be a field, and consider the hypercube in . Sziklai and Weiner (Journal of Combinatorial Theory, Series A 2022) showed that if a p…
Stabbing boxes with finitely many axis-parallel lines and flats
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi
In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in to be pierceable by finitely many axis-p…