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Search: id:A047884
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| A047884 |
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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 increasing subsequence is k. |
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4
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| 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; listen)
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OFFSET
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1,5
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REFERENCES
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W. Fulton, Young Tableaux, Cambridge, 1997.
D. Stanton and D. White, Constructive Combinatorics, Springer, 1986.
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LINKS
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Index entries for sequences related to Young tableaux.
R. P. Stanley, A combinatorial miscellany
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EXAMPLE
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1; 1,1; 1,2,1; 1,5,3,1; 1,9,11,4,1; ...
For n=3 the 4 tableaux are
1 2 3 . 1 2 . 1 3 . 1
. . . . 3 . . 2 . . 2
. . . . . . . . . . 3
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MATHEMATICA
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Table[ Plus@@( NumberOfTableaux/@ Reverse/@Union[ Sort/@(Compositions[ n-m, m ]+1) ]), {n, 12}, {m, n} ]
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CROSSREFS
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Row sums give A000085. Cf. A049400, A049401.
Sequence in context: A107735 A137570 A079213 this_sequence A124328 A055818 A106240
Adjacent sequences: A047881 A047882 A047883 this_sequence A047885 A047886 A047887
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KEYWORD
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nonn,tabl,nice,easy
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AUTHOR
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wouter.meeussen(AT)pandora.be
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