2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69450We 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.In french, to appear in Comptes rendus de l'Academie des SciencesCombinatoricsGroup Theory05C25, 52C35text