  Given a triangulated 2-Calabi-Yau category C and a cluster-tilting
subcategory T, the index of an object X of C is a certain element of the
Grothendieck group of the additive category T. In this note, we show that a
rigid object of C is determined by its index, that the indices of the
indecomposables of a cluster-tilting subcategory T' form a basis of the
Grothendieck group of T and that, if T and T' are related by a mutation, then
the indices with respect to T and T' are related by a certain piecewise linear
transformation introduced by Fomin and Zelevinsky in their study of cluster
algebras with coefficients. This allows us to give a combinatorial construction
of the indices of all rigid objects reachable from the given cluster-tilting
subcategory T. Conjecturally, these indices coincide with Fomin-Zelevinsky's
g-vectors.
