Adrian Dumitrescu

activity

20242026

collaborators

14 papers

math.CO2026

The number of regular simplices in higher dimensions

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

We study the extremal function $S_{d}^{k} (n)$ , defined as the maximum number of regular $(k - 1)$ -simplices spanned by $n$ points in $R^{d}$ . For any fixed $d \geq 2 k \geq 6$ , we dete…

math.CO2026

On multiplicities of interpoint distances

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

Given a set $X \subseteq R^{2}$ of $n$ points and a distance $d > 0$ , the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$ . Let $a_1(X)…

math.CO2026

Covering Complete Geometric Graphs by Monotone Paths

Adrian Dumitrescu, JÃ¡nos Pach, Morteza Saghafian +1

Given a set $A$ of $n$ points (vertices) in general position in the plane, the \emph{complete geometric graph} $K_{n} [A]$ consists of all $(2 n)$ segments (edges) between the…

cs.CG2025

A Couple of Simple Algorithms for $k$ -Dispersion

Ke Chen, Adrian Dumitrescu

Given a set $P$ of $n$ points in $R^{d}$ , and a positive integer $k \leq n$ , the $k$ -dispersion problem is that of selecting $k$ of the given points so that the minimum inte…

math.CO2025

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to it…

math.CO2025

Note on the Number of Almost Ordinary Triangles

Adrian Dumitrescu, JÃ¡nos Pach

Let $X$ be a set of $n$ points in the plane, not all on a line. According to the Gallai-Sylvester theorem, $X$ always spans an \emph{ordinary line}, i.e., one that passes through p…

The number of regular simplices in higher dimensions

On multiplicities of interpoint distances

Covering Complete Geometric Graphs by Monotone Paths

A Couple of Simple Algorithms for k-Dispersion

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

Note on the Number of Almost Ordinary Triangles

A Couple of Simple Algorithms for $k$ -Dispersion