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.
The F-triangle of the generalised cluster complex
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.
The following versions are available:
Back to Christian Krattenthaler's