B. McDonald

activity

20142023

most citedGaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

10 citations · 14 across the 10 of their papers we have counts for

collaborators

11 papers

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

VC-Dimension and Distance Chains in $F_{q}^{d}$

Ruben Ascoli, Livia Betti, Justin Cheigh +8

Given a domain $X$ and a collection $H$ of functions $h : X \to {0, 1}$ , the Vapnik-Chervonenkis (VC) dimension of $H$ measures its complexity in an appropriate s…

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…

math.NT2015★ 1 cited

Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . Previo…

math.NT2014

Benford Behavior of Generalized Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by $F_{1} = 1, F_{2} = 2$ and $F_{n + 1} = F_{n} + F_{n - 1}$ , every…

math.NT2014★ 3 cited

Gaps between zeros of GL(2) $L$ -functions

Owen Barrett, Brian McDonald, Steven J. Miller +3

Let $L (s, f)$ be an $L$ -function associated to a primitive (holomorphic or Maass) cusp form $f$ on GL(2) over $Q$ . Combining mean-value estimates of Montgomery and Vaughan…

math.NT2014★ 10 cited

Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . We con…

math.NT2014

Benford Behavior of Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers ${F_{i}}_{i = 1}^{\infty}$ . A set $S \subset \…

VC-Dimension of Hyperplanes over Finite Fields

VC-Dimension and Distance Chains in Fqd​

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

Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals

Benford Behavior of Generalized Zeckendorf Decompositions

Gaps between zeros of GL(2) L-functions

Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

Benford Behavior of Zeckendorf Decompositions

VC-Dimension and Distance Chains in $F_{q}^{d}$

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 $F_{q}^{d}$

Gaps between zeros of GL(2) $L$ -functions