The Bruhat order on a Coxeter group 
is the partial order in which
iff every
reduced word for 
contains some reduced word
for 
as a subword
(Björner and Brenti 2005, p. 34).
Bruhat Order
See also
Bruhat Graph, Combinatorial Invariance Conjecture, Coxeter Group, Kazhdan-Lusztig Polynomial, Partial Order, Permutation, Reduced Word, SubwordExplore with Wolfram|Alpha
References
Björner, A. and Brenti, F. Combinatorics of Coxeter Groups. New York: Springer-Verlag, 2005.Björner, A. and Wachs, M. "Bruhat Order of Coxeter Groups and Shellability." Adv. Math. 43, 87-100, 1982.Cite this as:
Weisstein, Eric W. "Bruhat Order." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BruhatOrder.html