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Article Dans Une Revue Journal of Algebraic Combinatorics Année : 2005

Balanced configurations of 2n+1 plane vectors

Résumé

A plane configuration {v_1,...,v_m} of vectors in {\mathbb R}^2 is said to be balanced if for any index i, the set of the det(v_i,v_j) for j\neq 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 GL_2({\mathbb R})-equivalent to a regular (2n+1)-gon. In this note, we prove this conjecture.

Dates et versions

hal-00122680 , version 1 (04-01-2007)

Identifiants

Citer

N. Ressayre. Balanced configurations of 2n+1 plane vectors. Journal of Algebraic Combinatorics, 2005, 21, pp.281-287. ⟨10.1007/s10801-005-6912-2⟩. ⟨hal-00122680⟩
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