$h$-Vectors of Generalized Associahedra and Noncrossing Partitions

Authors

Colum Watt, Technological University DublinFollow
Thomas Brady, Dublin City UniversityFollow
Christos A. Athanasiadis, University of AthensFollow
Jon McCammond, University of California, Santa BarbaraFollow

Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Pure mathematics

Publication Details

International Mathematical Research Notices, (2007), article ID 69705.

Abstract

A uniform proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice $\mathbf{L}$ of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice $\mathbf{L}$ in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.

DOI

https://doi.org/10.1155/IMRN/2006/69705

Recommended Citation

Watt, C., Brady, T. & Athanasiadis, C. (2007). $h$-Vectors of Generalized Associahedra and Noncrossing Partitions. International Mathematical Research Notices, vol. 1, no. 29, article ID 69705. doi:10.1155/IMRN/2006/69705