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 On the H-triangle of generalised nonnesting partitions


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To a crystallographic root system \Phi, and a positive integer k, there are associated two Fuss-Catalan objects, the set of nonnesting partitions NN^k\Phi, and the cluster complex \Delta^k\Phi. These posess a number of enumerative coincidences, many of which are captured in the H=F conjecture, first posed by Chapoton for k=1 and later generalized to k1 by Armstrong. We prove this conjecture in the case where either k=1 or \Phi is a classical root system.



Author: Marko Thiel

Source: https://archive.org/



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