J. Passant

activity

20172025

most citedFinite point configurations in the plane, rigidity and Erdos problems

1 citations · 4 across the 7 of their papers we have counts for

collaborators

7 papers

math.CO2025

Generalised Erdős distance theory on graphs

Sean Dewar, Nora Frankl, Samuel Mansfield +3

The famous Erdős distinct distances problem asks the following: how many distinct distances must exist between a set of $n$ points in the plane? There are many generalisations of t…

math.CO2024

On Distinct Angles in the Plane

Sergei V. Konyagin, Jonathan Passant, Misha Rudnev

We prove that if $N$ points lie in convex position in the plane then they determine $Ω (N^{5/4})$ distinct angles, provided that the points do not lie on a common circle. This is de…

math.CO2022★ 1 cited

A Structural Theorem for Sets With Few Triangles

Sam Mansfield, Jonathan Passant

We show that if a finite point set $P \subseteq R^{2}$ has the fewest congruence classes of triangles possible, up to a constant $M$ , then at least one of the following holds…

math.CO2020★ 1 cited

On Erdős Chains in the Plane

Jonathan Passant

Let $P$ be a finite point set in $R^{2}$ with the set of distance $n$ -chains defined as $Δ_{n} (P) = {(∣ p_{1} - p_{2} ∣, ∣ p_{2} - p_{3} ∣, \dots, ∣ p_{n} - p_{n + 1} ∣) : p_{i} \in P} .$ We show that fo…

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.CO2018★ 1 cited

Finite point configurations in the plane, rigidity and Erdos problems

A. Iosevich, J. Passant

For a finite point set $E \subset R^{d}$ and a connected graph $G$ on $k + 1$ vertices, we define a $G$ -framework to be a collection of $k + 1$ points in E such that the distan…