On a duality in Coxeter groups

被引:1
|
作者
Marietti, Mario [1 ]
机构
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
关键词
D O I
10.1016/j.ejc.2007.12.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In [R.P. Stanley, The descent set and connectivity set of a permutation, J. Integer Seq. 8 (3) (2005) Article 05.3.8] Stanley gives certain enumerative identities revealing a duality between descent sets and connectivity sets of the symmetric group. In this paper we generalize these identities to all Coxeter groups. The proofs are obtained by giving these identities an algebraic explanation in terms of parabolic Subgroups, coset representatives, and Poincare series, and by a formal argument in terms of inclusion-exclusion-like matrices. (c) 2007 Elsevier Ltd. All rights reserved.
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页码:1555 / 1562
页数:8
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