The F-triangle of the generalised cluster complex
Christian Krattenthaler
Abstract
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 Möbius function of his m-divisible partition poset associated to a finite root system.
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