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.

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

Author

Alois P. Heinz, Jul 12 2017

Keywords

• nonn
• tabf

Examples

			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;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..10, flattened
• R. P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin., 5 (1984), 359-372.

Crossrefs

Row sums give A246865.

Cf. A000217, A005118, A008302.

Formula

T(n,n*(n-1)/2) = A005118(n).