A263407 Triangle read by rows: T(n,k) (n>=2, k>=1) is the number of standard tableaux of size n and having k standard tableau in its orbit under promotion.

2, 2, 2, 2, 2, 6, 2, 6, 6, 12, 2, 4, 6, 12, 40, 0, 0, 0, 0, 0, 0, 12

Offset

2,1

Comments

Row sums give A000085, n >= 2.

The promotion operator, applied to a standard tableau t, does the following:

Remove the letter n from t, thus leaving a hole where it used to be. Apply jeu de taquin to move this hole southwest (in French notation) until it reaches the inner boundary of t. Fill 0 into the hole once jeu de taquin has completed. Finally, add 1 to each letter in the tableau. The resulting standard tableau is the image of t under the promotion operator.

Links

Table of n, a(n) for n=2..23.

FindStat - Combinatorial Statistic Finder, The orbit size of a standard tableau under promotion.

Mark D. Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discrete Mathematics 99 (1992), 79-113.

Sage Documentation, Tableaux.

Example

Triangle begins:
2,
2,2,
2,2,6,
2,6,6,12,
2,4,6,12,40,0,0,0,0,0,0,12,
...

Crossrefs

Cf. A000085.

Sequence in context: A278247 A160762 A112968 * A221838 A343122 A338869

Adjacent sequences: A263404 A263405 A263406 * A263408 A263409 A263410

Keyword

nonn,tabf,more

Author

Christian Stump, Oct 17 2015

Status

approved