The $F$-triangle of the generalised cluster complex

Details The $F$-triangle of the generalised cluster complex The $F$-triangle of the generalised cluster complex

2005-09-03

arxiv.org/abs/math/0509063v5

in: "Topics in Discrete Mathematics," dedicated to Jarik Nesetril on the occasion of his 60th birthday, M. Klazar, J. Kratochv

Mathematics

Combinatorics

AmS-TeX, 30 pages; style of equation numbering changed to the style in the printed publication

Scientific paper

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.

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