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math.CO2023
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…
math.CO2023★ 1 cited
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…
math.CO2023
On higher multiplicity hyperplane and polynomial covers for symmetry preserving subsets of the hypercube
Arijit Ghosh, Chandrima Kayal, Soumi Nandi +1
Alon and Füredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of…