## Thiel, Marko - On the $H$-triangle of generalised nonnesting partitions

dmtcs:2382 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
On the $H$-triangle of generalised nonnesting partitions

Authors: Thiel, Marko

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 : oai:HAL:hal-01207593v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: 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]