The sorting order on a Coxeter group
نویسندگان
چکیده
منابع مشابه
The sorting order on a Coxeter group
Let (W,S) be an arbitrary Coxeter system. For each sequence ω = (ω1, ω2, . . .) ∈ S∗ in the generators we define a partial order—called the ω-sorting order—on the set of group elements Wω ⊆ W that occur as finite subwords of ω. We show that the ω-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, t...
متن کاملA note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
متن کاملOn the Center of a Coxeter Group
In this paper, we show that the center of every Coxeter group is finite and isomorphic to (Z2) n for some n ≥ 0. Moreover, for a Coxeter system (W, S), we prove that Z(W ) = Z(W S\S̃) and Z(W S̃ ) = 1, where Z(W ) is the center of the Coxeter group W and S̃ is the subset of S such that the parabolic subgroup W S̃ is the essential parabolic subgroup of (W, S) (i.e. W S̃ is the minimum parabolic subgr...
متن کاملThe Order Dimension of Bruhat Order on Infinite Coxeter Groups
We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group Ãn. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.
متن کاملA Result on the Bruhat Order of a Coxeter Groups
§1 THE PROOF OF THEOREM 1. Fix a Coxeter group (W,S). The terminolog “ an expression of W ”means an element of W being written as a product of elements of S. We say an expression w of W is reduced if w is a product of `(w) elements of S. Given two expressions s1s2 · · · sk and t1t2 · · · tm of W with si, tj ∈ S, we write s1s2 · · · sk ≡ t1t2 · · · tm if otherwise. We say that two expressions g ...
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 Combinatorial Theory, Series A
سال: 2009
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.03.009