Unitarily invariant valuations and Tutte's sequence

Abstract

We prove Fu's power series conjecture which relates the algebra of isometry invariant valuations on complex space forms to a formal power series from combinatorics which was introduced by Tutte. The $n$-th coefficient of this series is the number of triangulations of a triangle with $3n$ internal edges; or the number of intervals in Tamari's lattice $Y_n$.