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A003040
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Highest degree of an irreducible representation of symmetric group S_n of degree n.
(Formerly M0811)
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9
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1, 1, 2, 3, 6, 16, 35, 90, 216, 768, 2310, 7700, 21450, 69498, 292864, 1153152, 4873050, 16336320, 64664600, 249420600, 1118939184, 5462865408, 28542158568, 117487079424, 547591590000, 2474843571200, 12760912164000, 57424104738000, 295284192952320
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OFFSET
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1,3
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COMMENTS
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Highest number of standard tableaux of the Ferrers diagrams of the partitions of n. Example: a(4) = 3 because to the partitions 4, 31, 22, 211, and 1111 there correspond 1, 3, 2, 3, and 1 standard tableaux, respectively. - Emeric Deutsch, Oct 02 2015
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REFERENCES
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.
D. E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups. 2nd ed., Oxford University Press, 1950, p. 265.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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a(5) = 6 because the degrees for S_5 are 1,1,4,4,5,5,6.
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PROG
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(Sage)
res = 1
for P in Partitions(n):
res = max(res, P.dimension())
return res
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CROSSREFS
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A117500 gives the corresponding partitions of n.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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