6 papers
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…
No Infinite -Theorem for Piercing Compact Convex Sets with Lines in
Sutanoya Chakraborty, Arijit Ghosh
An infinite -theorem, or an -theorem, involving two families and of sets, states that if in every infinite subset of ,…
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…
Language Models are Crossword Solvers
Soumadeep Saha, Sutanoya Chakraborty, Saptarshi Saha +1
Crosswords are a form of word puzzle that require a solver to demonstrate a high degree of proficiency in natural language understanding, wordplay, reasoning, and world knowledge,…
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…