h-Vectors of generalized associahedra and noncrossing partitions

Christos A. Athanasiadis; Thomas Brady; Jon McCammond; Colum Watt

doi:10.1155/IMRN/2006/69705

h-Vectors of generalized associahedra and noncrossing partitions

Christos A. Athanasiadis
, Thomas Brady
, Jon McCammond
, Colum Watt

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	69705
Journal	International Mathematics Research Notices
Volume	2006
DOIs	https://doi.org/10.1155/IMRN/2006/69705
Publication status	Published - 2006

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title = "h-Vectors of generalized associahedra and noncrossing partitions",

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

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AU - Athanasiadis, Christos A.

AU - Brady, Thomas

AU - McCammond, Jon

AU - Watt, Colum

PY - 2006

Y1 - 2006

N2 - A uniform proof is given that the entries of theh-vector of the cluster complex (Φ), associated by S. Fomin and A. Zelevinsky to a finite root system Φ, count elements of the lattice L of noncrossing partitions of corresponding type by rank. Similar interpretations for theh-vector of the positive part of (Φ) are provided.The proof utilizes the appearance of the complex (Φ) in the context of the lattice L in recent work of two of the authors, as well as an explicit shelling of (Φ).

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

UR - https://www.scopus.com/pages/publications/33746871505

U2 - 10.1155/IMRN/2006/69705

DO - 10.1155/IMRN/2006/69705

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SN - 1073-7928

VL - 2006

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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ER -

h-Vectors of generalized associahedra and noncrossing partitions

Abstract

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