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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. 0
2, 2, 2, 2, 2, 6, 2, 6, 6, 12, 2, 4, 6, 12, 40, 0, 0, 0, 0, 0, 0, 12 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)