منابع مشابه
Descent Systems for Bruhat Posets
Let (W,S) be a finite Weyl group and let w ∈ W . It is widely appreciated that the descent set D(w) = {s ∈ S | l(ws) < l(w)} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset W J where J ⊂ S. Our main results here include the identification of a certain subset S ⊂ W J that convinci...
متن کاملS ep 2 00 8 Descent Systems for Bruhat Posets Lex E . Renner March 2008
Let (W,S) be a finite Weyl group and let w ∈ W . It is widely appreciated that the descent set D(w) = {s ∈ S | l(ws) < l(w)} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset W J where J ⊆ S. Our main results here include the identification of a certain subset S ⊆ W J that convinci...
متن کاملOn Bruhat posets associated to compositions ∗
The purpose of this work is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes. Résumé. ...
متن کاملBruhat order on plane posets and applications
A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space HPP generated by PP , using the notion of biideals of plane posets. We here define a partial order on PP , making it isomorphic to the set of partitions with t...
متن کاملOrder Dimension, Strong Bruhat Order and Lattice Properties for Posets
We determine the order dimension of the strong Bruhat order on finite Coxeter groups of types A, B and H. The order dimension is determined using a generalization of a theorem of Dilworth: dim(P ) = width(Irr(P )), whenever P satisfies a simple order-theoretic condition called here the dissective property (or “clivage” in [16, 21]). The result for dissective posets follows from an upper bound a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2008
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-008-0141-4