|
| |
|
|
A047884
|
|
Triangle of numbers a(n,k) = number of Young tableaux with n cells and k rows (1<=k<=n); also number of self-inverse permutations on n letters in which the length of the longest scattered (i.e. not necessarily contiguous) increasing subsequence is k.
|
|
5
| |
|
|
1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 9, 11, 4, 1, 1, 19, 31, 19, 5, 1, 1, 34, 92, 69, 29, 6, 1, 1, 69, 253, 265, 127, 41, 7, 1, 1, 125, 709, 929, 583, 209, 55, 8, 1, 1, 251, 1936, 3356, 2446, 1106, 319, 71, 9, 1, 1, 461, 5336, 11626, 10484, 5323, 1904, 461, 89, 10, 1
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
REFERENCES
| W. Fulton, Young Tableaux, Cambridge, 1997.
D. Stanton and D. White, Constructive Combinatorics, Springer, 1986.
|
|
|
LINKS
| Index entries for sequences related to Young tableaux.
R. P. Stanley, A combinatorial miscellany
|
|
|
EXAMPLE
| For n=3 the 4 tableaux are
1 2 3 . 1 2 . 1 3 . 1
. . . . 3 . . 2 . . 2
. . . . . . . . . . 3
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 5, 3, 1;
1, 9, 11, 4, 1;
1, 19, 31, 19, 5, 1;
1, 34, 92, 69, 29, 6, 1;
1, 69, 253, 265, 127, 41, 7, 1;
1, 125, 709, 929, 583, 209, 55, 8, 1;
1, 251, 1936, 3356, 2446, 1106, 319, 71, 9, 1;
1, 461, 5336, 11626, 10484, 5323, 1904, 461, 89, 10, 1;
|
|
|
MATHEMATICA
| Table[ Plus@@( NumberOfTableaux/@ Reverse/@Union[ Sort/@(Compositions[ n-m, m ]+1) ]), {n, 12}, {m, n} ]
|
|
|
CROSSREFS
| Row sums give A000085. Cf. A049400, A049401, and A178249 which imposes contiguity.
Sequence in context: A107735 A137570 A079213 * A124328 A055818 A106240
Adjacent sequences: A047881 A047882 A047883 * A047885 A047886 A047887
|
|
|
KEYWORD
| nonn,tabl,nice,easy
|
|
|
AUTHOR
| wouter.meeussen(AT)pandora.be
|
|
|
EXTENSIONS
| Definition amended ('scattered' added) by Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 22 2010
|
| |
|
|
