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Search: id:A003040
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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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+0
7
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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, 295284192942320
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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S. Come't, Improved methods to calculate the characters of the symmetric group, Math. Comp. 14 (1960) 104-117.
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.
J. McKay, The largest degrees of irreducible characters of the symmetric group. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 terms.)
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LINKS
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J. McKay, Page 1 of 5 pages of tables from Math. Comp. paper
J. McKay, Page 2 of 5 pages of tables from Math. Comp. paper
J. McKay, Page 3 of 5 pages of tables from Math. Comp. paper
J. McKay, Page 4 of 5 pages of tables from Math. Comp. paper
J. McKay, Page 5 of 5 pages of tables from Math. Comp. paper
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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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CROSSREFS
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A117500 gives the corresponding partitions of n.
Cf. A003869, A003870, A003871, A003872, A003873, A003874, A003875, A003876, A003877.
Sequence in context: A109162 A028688 A030753 this_sequence A126317 A079437 A061220
Adjacent sequences: A003037 A003038 A003039 this_sequence A003041 A003042 A003043
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KEYWORD
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nonn
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AUTHOR
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njas, R. P. Stanley
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EXTENSIONS
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Entry revised and extended by njas, Apr 28 2006
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