Shellability of noncrossing partition lattices

被引：32
作者：
Athanasiadis, Christos A.
Brady, Thomas
Watt, Colum
机构：
[1] Univ Crete, Dept Math, Iraklion 71409, Greece
[2] Dublin City Univ, Dept Math Sci, Dublin 9, Ireland
[3] Dublin Inst Technol, Sch Math, Dublin 8, Ireland
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 04期
关键词：
noncrossing partitions; real reflection group; partially ordered set; shellability; Coxeter element; reflection ordering;
D O I：
10.1090/S0002-9939-06-08534-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type D-n and those of exceptional type and rank at least three.
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收藏
页码：939 / 949
页数：11
相关论文
共 20 条
[1]   On a refinement of the generalized Catalan numbers for Weyl groups [J].
Athanasiadis, CA .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (01) :179-196
[2]   Noncrossing partitions for the group Dn [J].
Athanasiadis, CA ;
Reiner, V .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2004, 18 (02) :397-417
[3]   The dual braid monoid [J].
Bessis, D .
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2003, 36 (05) :647-683
[4]   SHELLABLE AND COHEN-MACAULAY PARTIALLY ORDERED SETS [J].
BJORNER, A .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 260 (01) :159-183
[5]  
Bjorner A., 2005, Graduate Texts in Mathematics, V231, DOI 10.1007/3-540-27596-7
[6]   K(π, 1)'s for Artin groups of finite type [J].
Brady, T ;
Watt, C .
GEOMETRIAE DEDICATA, 2002, 94 (01) :225-250
[7]   A partial order on the symmetric group and new K(π,1)′s for the braid groups [J].
Brady, T .
ADVANCES IN MATHEMATICS, 2001, 161 (01) :20-40
[8]  
BRADY T, 2005, IN PRESS T AM MATH S
[9]  
Chapoton F., 2004, S M LOTHAR COMBIN, V51
[10]   Y-systems and generalized associahedra [J].
Fomin, S ;
Zelevinsky, A .
ANNALS OF MATHEMATICS, 2003, 158 (03) :977-1018
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