2 papers
math.CO2020
Dot product chains
Shelby Kilmer, Caleb Marshall, Steven Senger
We study a variant of Erd\H os' unit distance problem, concerning dot products between successive pairs of points chosen from a large finite point set. Specifically, given a large…
math.GR2014
A sharper threshold for random groups at density one-half
Moon Duchin, Kasia Jankiewicz, Shelby C. Kilmer +3
In the density model of random groups, we consider presentations with any fixed number m of generators and many random relators of length l, sending l to infinity. If d is a "densi…