5 papers · 1 filter
Bounds on point configurations determined by distances and dot products
Slade Gunter, Eyvi Palsson, Ben Rhodes +1
We study a family of variants of Erd\H os' unit distance problem, concerning distances and dot products between pairs of points chosen from a large finite point set. Specifically,…
Counting Restricted Partitions of Integers into Fractions: Symmetry and Modes of the Generating Function and a Connection to
Zachary Hoelscher, Eyvindur Ari Palsson
Motivated by the study of integer partitions, we consider partitions of integers into fractions of a particular form, namely with constant denominators and distinct odd or even num…
Tinkering with Lattices: A New Take on the Erdős Distance Problem
Elzbieta Boldyriew, Elena Kim, Steven J. Miller +4
The Erdős distance problem concerns the least number of distinct distances that can be determined by points in the plane. The integer lattice with points is known as \texti…
Discrete maximal operators over surfaces of higher codimension
Theresa C. Anderson, Eyvindur Ari Palsson, Angel V. Kumchev
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analy…
Supercritical discrete restriction estimates for forms in many variables
Brian Cook, Kevin Hughes, Eyvindur Palsson
We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmet…