Work

An improved bound on the number of dot products determined by a finite point set in the plane

Year: 2026

Type: article

Abstract: We are interested to bound from below the number of distinct dot products determined by a finite set of points P in the Euclidean plane. In this paper, we build on [3] to obtain the improved lower bound | { p ⋅ q : p , q ∈ P } | ≳ | P | 2 3 + 7 1425 .

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115399

Author: Michalis Kokkinos

Institution: Johannes Kepler University of Linz

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funder: Austrian Science Fund