Balanced configurations of 2n+1 plane vectors

2002/06/24 by Nicolas Ressayre, N. Ressayre, Ressayre, N.
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.AG #math.CO #math.RA

paper · pdf · doi:10.48550/arxiv.math/0206234

7 pages, no figure

arxiv created 2002/06/24 · openalex publication_date 2002/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A plane configuration v₁,...,v_m of vectors in \mathbb R² is said to be balanced if for any index i, the set of the det(v_i,v_j) for j≠ i is symmetric around the origin. A plane configuration is said to be uniform if every pair of vectors is linearly independent. E. Cattani and A. Dickenstein conjectured that any uniform balanced configuration is GL₂(\mathbb R)-equivalent to a regular (2n+1)-gon. In this note, we prove this conjecture.

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