This material has been published in "Topics in Discrete Mathematics,"
dedicated to Jarik Nesetril on the occasion of his 60th birthday,
M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas and
P. Valtr, eds., Springer-Verlag, Berlin, New York, 2006, pp. 93-126,
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Christian Krattenthaler
The F-triangle of the generalised cluster complex
(30 pages)
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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