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, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Springer-Verlag. This material may not be copied or reposted without explicit permission.

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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