h-vectors of generalized associahedra and noncrossing partitions

被引：15

作者：

Athanasiadis, Christos A. ^{[1
]}

Brady, Thomas

McCammond, Jon

Watt, Colum

机构：

[1] Univ Athens, Dept Math, Div Algebra & Geometry, Athens 15784, Greece

[2] Dublin City Univ, Sch Math Sci, Dublin 9, Ireland

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[4] Dublin Inst Technol, Sch Math Sci, Dublin 8, Ireland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2006年 / 2006卷

关键词：

D O I：

10.1155/IMRN/2006/69705

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 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 L in recent work of two of the authors, as well as an explicit shelling of Delta(Phi).

引用

页数：28

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