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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
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
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 * A377059 A221838 A343122
KEYWORD
nonn,tabf,more
AUTHOR
Christian Stump, Oct 17 2015
STATUS
approved