Combinatoire
Le cocycle du verger
[The orchard cocycle]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 187-190.

We define and prove uniqueness of a natural homomorphism (called the Orchard morphism) from some groups associated naturally to a finite set E to the group (E) of two-partitions of E representing equivalence relations having at most two classes on E. As an application, given a finite generic configuration 𝒞R d , we exhibit a natural partition of 𝒞 in two sets.

Le but de cette Note est de montrer l'existence et l'unicité d'un homomorphisme naturel non-trivial entre certains groupes associés à un ensemble fini. Cet homomorphisme fournit une partition naturelle en deux sous-ensembles sur l'ensemble 𝒞R d des points d'une configuration finie générique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.11.021
Bacher, Roland 1

1 Institut Fourier, laboratoire de mathématiques, UMR 5582 (UJF-CNRS), BP 74, 38402 St Martin d'Hères cedex, France
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Bacher, Roland. Le cocycle du verger. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 187-190. doi : 10.1016/j.crma.2003.11.021. http://www.numdam.org/articles/10.1016/j.crma.2003.11.021/

[1] Bacher, R.; Garber, D. Chromatic properties of generic planar configurations of points (Preprint) | arXiv

[2] Bredon, G.E. Topology and Geometry, Springer, 1993

[3] Massey, W.S. A Basic Course in Algebraic Topology, Springer, 1991

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