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.
CITATION STYLE
Krattenthaler, C. (2007). The F-triangle of the Generalised Cluster Complex. In Topics in Discrete Mathematics (pp. 93–126). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-33700-8_6
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