# On the $H$-triangle of generalised nonnesting partitions

Abstract : 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.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [12 references]

https://hal.inria.fr/hal-01207593
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, October 1, 2015 - 9:28:59 AM
Last modification on : Saturday, April 11, 2020 - 6:38:03 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:43:36 AM

### File

dmAT0108.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01207593, version 1

### Citation

Marko Thiel. On the $H$-triangle of generalised nonnesting partitions. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.83-90. ⟨hal-01207593⟩

Record views