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A289778
Number T(n,k) of reduced decompositions for all permutations of [n] with exactly k inversions; triangle T(n,k), n>=0, 0<=k<=n*(n-1)/2, read by rows.
3
1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 6, 10, 14, 16, 16, 1, 4, 12, 30, 68, 132, 252, 412, 614, 768, 768, 1, 5, 20, 68, 210, 588, 1540, 3778, 8768, 19402, 40284, 78276, 137236, 219362, 292864, 292864, 1, 6, 30, 130, 512, 1864, 6340, 20472, 62770, 184748, 521272, 1428932
OFFSET
0,6
LINKS
R. P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin., 5 (1984), 359-372.
FORMULA
T(n,n*(n-1)/2) = A005118(n).
EXAMPLE
Triangle T(n,k) begins:
1;
1;
1, 1;
1, 2, 2, 2;
1, 3, 6, 10, 14, 16, 16;
1, 4, 12, 30, 68, 132, 252, 412, 614, 768, 768;
...
CROSSREFS
Row sums give A246865.
Sequence in context: A127496 A376626 A350189 * A277523 A144393 A351112
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Jul 12 2017
STATUS
approved