B. McDonald

activity

20202022

collaborators

4 papers

math.CO2022

Dot products in $F_{q}^{3}$ and the Vapnik-Chervonenkis dimension

A. Iosevich, B. McDonald, M. Sun

Given a set $E \subset F_{q}^{3}$ , where $F_{q}$ is the field with $q$ elements. Consider a set of "classifiers" $H_{t}^{3} (E) = {h_{y} : y \in E}$ , where $h_{y} (x) = 1$ if…

math.CO2021

The VC-dimension and point configurations in $F_{q}^{2}$

D. Fitzpatrick, A. Iosevich, B. McDonald +1

Let $X$ be a set and $H$ a collection of functions from $X$ to ${0, 1}$ . We say that $H$ shatters a finite set $C \subset X$ if the restriction of ${\mathcal…

math.CO2021

Cycles of arbitrary length in distance graphs on $F_{q}^{d}$

Alex Iosevich, Gail Jardine, Brian McDonald

For $E \subset F_{q}^{d}$ , $d \geq 2$ , where $F_{q}$ is the finite field with $q$ elements, we consider the distance graph $G_{t}^{d i s t} (E)$ , $t \neq = 0$ , where the…

math.MG2020

Distinct Distances Between a Circle and a Generic Set

Alex McDonald, Brian McDonald, Jonathan Passant +1

Let $S$ be a set of points in $R^{2}$ contained in a circle and $P$ an unrestricted point set in $R^{2}$ . We prove the number of distinct distances between points in…

Dot products in Fq3​ and the Vapnik-Chervonenkis dimension

The VC-dimension and point configurations in Fq2​

Cycles of arbitrary length in distance graphs on Fqd​

Distinct Distances Between a Circle and a Generic Set

Dot products in $F_{q}^{3}$ and the Vapnik-Chervonenkis dimension

The VC-dimension and point configurations in $F_{q}^{2}$

Cycles of arbitrary length in distance graphs on $F_{q}^{d}$