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

0,6

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.

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.

Cf. A000217, A005118, A008302.

Sequence in context: A004065 A127496 A350189 * A277523 A144393 A351112

Adjacent sequences: A289775 A289776 A289777 * A289779 A289780 A289781

Keyword

nonn,tabf

Author

Alois P. Heinz, Jul 12 2017

Status

approved