English

The $F$-triangle of the generalised cluster complex

Combinatorics 2007-05-23 v5 Representation Theory

Abstract

The FF-triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the FF-triangle explicitly for all irreducible finite root systems. Furthermore, we use these results to partially prove the "M=FM=F Conjecture" of Armstrong which predicts a surprising relation between the FF-triangle and the M\"obius function of his mm-divisible partition poset associated to a finite root system.

Keywords

Cite

@article{arxiv.math/0509063,
  title  = {The $F$-triangle of the generalised cluster complex},
  author = {Christian Krattenthaler},
  journal= {arXiv preprint arXiv:math/0509063},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:24:05.525Z