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The $F$-triangle of the generalised cluster complex

Christian Krattenthaler
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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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Christian Krattenthaler. 2006-02-09. The $F$-triangle of the generalised cluster complex. https://arxiv.org/abs/math/0509063

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