arXiv math/05090632005-09math.COmath.RT

The $F$-triangle of the generalised cluster complex

Christian Krattenthaler

备注：: AmS-TeX, 30 pages; style of equation numbering changed to the style in the printed publication
发表信息：: 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.

英文摘要：

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.

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