B. McDonald

activity

20202023

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4 papers · 1 filter

math.CO2023

VC-Dimension of Hyperplanes over Finite Fields

Ruben Ascoli, Livia Betti, Justin Cheigh +8

Let $F_{q}^{d}$ be the $d$ -dimensional vector space over the finite field with $q$ elements. For a subset $E \subseteq F_{q}^{d}$ and a fixed nonzero $t \in F_{q}$ ,…

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…

VC-Dimension of Hyperplanes over Finite Fields

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​

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 $F_{q}^{d}$