76.11 CoxeterElementsLength

CoxeterElementsLength( W, l )

returns as a list of permutations the list of all elements of W of length l.

    gap> W := CoxeterGroup( "G", 2 );;
    gap> e := CoxeterElementsLength( W, 6 );
    [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ]
    gap> e[1] = LongestCoxeterElement( W );
    true 

The result of the computation of elements of a given length is stored in the component elts of the record of W. Thus W.elts[lw+1] contains the list of all elements of length lw in W. There are a number of Kazhdan-Lusztig polynomials and bases) which refer to the ordering of the elements in these lists in W.elts.

This function requires the package "chevie" (see RequirePackage).

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