Alex McDonald

activity

20192021

collaborators

5 papers

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…

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

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