  The $F$-triangle is a refined face count for the generalised cluster complex
of Fomin and Reading. We compute the $F$-triangle explicitly for all
irreducible finite root systems. Furthermore, we use these results to partially
prove the "$M=F$ Conjecture" of Armstrong which predicts a surprising relation
between the $F$-triangle and the M\"obius function of his $m$-divisible
partition poset associated to a finite root system.
