Abstract
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 “F = M 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.
Research partially supported by EC’S IHRP Programme, grant HPRN-CT-2001-00272, “Algebraic Combinatorics in Europe.”
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Krattenthaler, C. (2006). The F-triangle of the Generalised Cluster Complex. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_6
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DOI: https://doi.org/10.1007/3-540-33700-8_6
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