A263408 Triangle read by rows: T(n>=1, k>=0) is the number of standard tableaux of size n and (Haglund and Stevens) inversion number k.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 3, 2, 1, 1

Offset

1,10

Comments

Row sums give A000085, n >= 2.

The inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b).

Links

Table of n, a(n) for n=1..18.

FindStat - Combinatorial Statistic Finder, The inversion number of a standard tableau as defined by Haglund and Stevens.

J. Haglund and L. Stevens, An extension of the Foata map to standard Young tableaux, Séminaire Lotharingien de Combinatoire 56 (2006), Article B56c.

Example

Triangle begins:
1,1,
1,1,1,1,
1,1,2,3,4,4,4,3,2,1,1,
...

Crossrefs

Cf. A000085.

Sequence in context: A366681 A241283 A274095 * A109870 A364368 A171502

Adjacent sequences: A263405 A263406 A263407 * A263409 A263410 A263411

Keyword

nonn,tabf,more

Author

Christian Stump, Oct 17 2015

Status

approved