Le cocycle du verger

Details Le cocycle du verger Le cocycle du verger

2003-12-03

arxiv.org/abs/math/0312079v1

Mathematics

Combinatorics

In french, to appear in Comptes rendus de l'Academie des Sciences

Scientific paper

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 ${\mathcal E}(E)$ of two-partitions of $E$ representing equivalence relations having at most two classes on $E$. As an application, given a finite generic configuration ${\mathcal C}\subset {\mathbf R}^d$, we exhibit a natural partition of ${\mathcal C}$ in two sets.

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