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Discrete Mathematics & Theoretical Computer Science |
With a crystallographic root system $\Phi$ , there are associated two Catalan objects, the set of nonnesting partitions $NN(\Phi)$, and the cluster complex $\Delta (\Phi)$. 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 $NN^{(k)}(\Phi)$ and $\Delta^{(k)}(\Phi)$, conjectured by Armstrong.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0601676 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0601676
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