On the $H$-triangle of generalised nonnesting partitions

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 C...

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Bibliographic Details
Published in:Discrete Mathematics & Theoretical Computer Science
Main Author: Marko Thiel
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2014-01-01
Subjects:
noncrossing partitions
nonnesting partitions
coxeter-catalan objects
cluster complex
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
Online Access:https://dmtcs.episciences.org/2382/pdf
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Summary: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.
ISSN:1365-8050

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