A289778 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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

(list; graph; refs; listen; history; text; internal format)

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: A127496 A376626 A350189 * A277523 A144393 A351112

Adjacent sequences: A289775 A289776 A289777 * A289779 A289780 A289781

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Jul 12 2017

STATUS

approved