Alex McDonald

activity

20192026

most citedInfinite constant gap length trees in products of thick Cantor sets

5 citations · 5 across the 7 of their papers we have counts for

collaborators

10 papers

math.CO2026

VC-dimension of distance graphs in finite field geometries

Brian McDonald Bakas, Moustapha Diallo, Alex McDonald

We study the VC-dimension of distance graphs of large subsets of vector spaces over finite fields. For $3 \leq k \leq d$ , we prove the distance graph of $E\subset \F_q^d$ has VC-dime…

math.CA2026

Extremal graph theory and point configurations in Ahlfors-David regular sets

Alex McDonald

We study the problem of embedding bipartite graphs in Ahlfors-David regular sets of large dimension using results from extremal graph theory. Our main theorem states that any graph…

math.CA2025

The VC-dimension and point configurations in $R^{d}$

Alex Iosevich, Akos Magyar, Alex McDonald +1

Given a set $X$ and a collection $H$ of functions from $X$ to ${0, 1}$ , the VC-dimension measures the complexity of the hypothesis class $H$ in the context of…

math.CA2022★ 5 cited

Infinite constant gap length trees in products of thick Cantor sets

Alex McDonald, Krystal Taylor

We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove that the set of choices for…

math.CA2021

Finite Point configurations in Products of Thick Cantor sets and a Robust Nonlinear Newhouse Gap Lemma

Alex McDonald, Krystal Taylor

In this paper we prove that the set of tuples of edge lengths in $K_{1} \times K_{2}$ corresponding to a finite tree has non-empty interior, where $K_{1}, K_{2} \subset R$ are Cantor…

math.CA2021

Volumes spanned by $k$ point configurations in $R^{d}$

Belmiro Galo, Alex McDonald

Given a $k$ -point configuration $x \in (R^{d})^{k}$ , we consider the $(d k)$ -vector of volumes determined by choosing any $d$ points of $x$ . We prove that a compact set…

math.CA2020

Areas spanned by point configurations in the plane

Alex McDonald

We consider an over-determined Falconer type problem on $(k + 1)$ -point configurations in the plane using the group action framework introduced in \cite{GroupAction}. We define the a…

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.CO2019

Areas of triangles and SL_2 actions in finite rings

Alex McDonald

In Euclidean space, one can use the dot product to give a formula for the area of a triangle in terms of the coordinates of each vertex. Since this formula involves only addition,…

math.CO2019

Congruence classes of large configurations in vector spaces over finite fields

Alex McDonald

Bennett, Hart, Iosevich, Pakianathan, and Rudnev found an exponent $s < d$ such that any set $E \subset F_{q}^{d}$ with $∣ E ∣ ≳ q^{s}$ determines $≳ q^{(2 k + 1)}$ c…

VC-dimension of distance graphs in finite field geometries

Extremal graph theory and point configurations in Ahlfors-David regular sets

The VC-dimension and point configurations in Rd

Infinite constant gap length trees in products of thick Cantor sets

Finite Point configurations in Products of Thick Cantor sets and a Robust Nonlinear Newhouse Gap Lemma

Volumes spanned by k point configurations in Rd

Areas spanned by point configurations in the plane

Distinct Distances Between a Circle and a Generic Set

Areas of triangles and SL_2 actions in finite rings

Congruence classes of large configurations in vector spaces over finite fields

The VC-dimension and point configurations in $R^{d}$

Volumes spanned by $k$ point configurations in $R^{d}$