Marko Thiel - 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) - https://doi.org/10.46298/dmtcs.2382
On the $H$-triangle of generalised nonnesting partitions

Authors: Marko Thiel 1

  • 1 Faculty of Mathematics [Vienna]

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.

https://doi.org/10.46298/dmtcs.2382
Source: 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
Imported 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]

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Source : ScholeXplorer IsRelatedTo ARXIV math/0601676
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0601676
  • 10.48550/arxiv.math/0601676
  • math/0601676
The $M$-triangle of generalised non-crossing partitions for the types $E_7$ and $E_8$

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