3 papers
math.MG2023
Explicit bounds for the layer number of the grid
Travis Dillon, Narmada Varadarajan
The number of steps required to exhaust a point set by iteratively removing the vertices of its convex hull is called the layer number of the point set. This article presents a sho…
math.NT2020
Pattern Problems related to the Arithmetic Kakeya Conjecture
Charlie Cowen-Breen, Elene Karangozishvili, Narmada Varadarajan +1
We study a variety of problems about homothets of sets related to the Kakeya conjecture. In particular, we show many of these problems are equivalent to the arithmetic Kakeya conje…
math.CO2019
Colouring bottomless rectangles and arborescences
Jean Cardinal, Kolja Knauer, Piotr Micek +3
We study problems related to colouring bottomless rectangles. One of our main results shows that for any positive integers , there is no semi-online algorithm that can -co…