Bruhat( W, y, w[, ly, lw] )
true, if the element y is less than or equal to the element
w of the Coxeter group W for the Bruhat order, and
(y is less than w if a reduced expression for y can be extracted
from one for w). Both y and w must be given as permutations on the
root vectors of W. The optional arguments ly, lw can contain the
length of the elements y and w. (In a computation with many calls to
Bruhat this may speed up the computation considerably.) See cite[(5.9)
and (5.10)]Hum90 for further properties of the Bruhat order.
gap> W := CoxeterGroup( "H", 3 );; gap> w := PermCoxeterWord( W, [ 1, 2, 1, 3 ] );; gap> b := Filtered( Elements( W ), i -> Bruhat( W, i, w, > CoxeterLength( W, i ), 4 ) );; gap> List( b, x -> CoxeterWord( W, x ) ); [ [ ], [ 3 ], [ 2 ], [ 2, 1 ], [ 2, 3 ], [ 2, 1, 3 ], [ 1 ], [ 1, 3 ], [ 1, 2 ], [ 1, 2, 1 ], [ 1, 2, 3 ], [ 1, 2, 1, 3 ] ]
This function requires the package "chevie" (see RequirePackage).
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