The $F$-triangle of the generalised cluster complex
Abstract
Description
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.
AmS-TeX, 30 pages; style of equation numbering changed to the style in the printed publication
AmS-TeX, 30 pages; style of equation numbering changed to the style in the printed publication
Citation
Consulte el texto completo en el siguiente enlace:
https://arxiv.org/abs/math/0509063
http://arxiv.org/abs/math/0509063
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.
http://arxiv.org/abs/math/0509063
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.