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On the H-triangle of generalised nonnesting partitions
With a crystallographic root system Φ, there are associated two Catalan objects, the set of nonnesting partitions N N (Φ), and the cluster complex ∆(Φ). These possess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton. We prove this conjecture, and indicate its generalisation for the Fuß-Catalan objects N N (k) (Φ) and ∆ (k) (Φ), conjectured by Armstrong. Résumé. ' A un système de racines cristallographique, on associe deuxfatcat:kycyf5urn5agtn7nlmjdhvsk7e