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math.CO2025
An asymptotic rigidity property from the realizability of chirotope extensions
Xavier Goaoc, Arnau Padrol
Let be a finite full-dimensional point configuration in . We show that if a point configuration has the property that all finite chirotopes realizable by addi…
math.CO2024
A colorful Goodman-Pollack-Wenger theorem
Andreas F. Holmsen
Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These co…
math.CO2024
No weak epsilon nets for lines and convex sets in space
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that there exist no weak -nets of constant size for lines and convex sets in .
math.CO2024
On a transversal theorem of Montejano and Karasev
Andreas F. Holmsen
We give a new proof of a theorem of Montejano and Karasev regarding -dimensional transversals to small families of convex sets. While their proof uses technical algebraic and to…