Alex McDonald

activity

20192026

collaborators

Showing math.CAShow all

4 papers · 1 filter

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.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…

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

The VC-dimension and point configurations in Rd

Volumes spanned by k point configurations in Rd

Areas spanned by point configurations in the plane

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

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