Steven Senger

most citedSharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains

9 citations · 10 across the 4 of their papers we have counts for

collaborators

4 papers

cs.MA2012

Reliability of swarming algorithms for mobile sensor network applications

Steven Senger

There are many well-studied swarming algorithms which are often suited to very specific purposes. As mobile sensor networks become increasingly complex, and are comprised of more a…

math.CO2010

A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries

David Covert, Derrick Hart, Alex Iosevich +2

We show that if $E \subset F_{q}^{d}$ , the $d$ -dimensional vector space over the finite field with $q$ elements, and $∣ E ∣ \geq ρ q^{d}$ , where $q^{- \frac{1}{2}} ≪ ρ \leq 1$ , the…

math.CA2010★ 1 cited

On sets of directions determined by subsets of $R^{d}$

Alex Iosevich, Mihalis Mourgoglou, Steven Senger

Given $E \subset R^{d}$ , $d \geq 2$ , define $D (E) \equiv (x - y) /∣ x - y ∣ : x, y \in E \subset S^{d - 1},$ the set of directions determined by $E$ . We prove that if the H…

math.CO2010★ 9 cited

Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains

Alex Iosevich, Steven Senger

In this paper we prove, for all $d \geq 2$ , that for no $s < \frac{d + 1}{2}$ does $I_{s} (μ) < \infty$ imply the canonical Falconer distance problem incidence bound, or the analogous estima…

Reliability of swarming algorithms for mobile sensor network applications

A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries

On sets of directions determined by subsets of Rd

Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains

On sets of directions determined by subsets of $R^{d}$