

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
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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), 79113.
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



