The $F$-triangle of the generalised cluster complex
Combinatorics
2007-05-23 v5 Representation Theory
Abstract
The -triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the -triangle explicitly for all irreducible finite root systems. Furthermore, we use these results to partially prove the " Conjecture" of Armstrong which predicts a surprising relation between the -triangle and the M\"obius function of his -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