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A003040 Highest degree of an irreducible representation of symmetric group S_n of degree n.
(Formerly M0811)
9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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
REFERENCES
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).
LINKS
Vasilii Duzhin, Table of n, a(n) for n = 1..153 (terms up to a(80) from Eric M. Schmidt)
J. McKay, The largest degrees of irreducible characters of the symmetric group. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 terms.)
J. McKay, Page 1 of 5 pages of tables from Math. Comp. paper [reports 29th term incorrectly]
Igor Pak, Greta Panova, and Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018.
EXAMPLE
a(5) = 6 because the degrees for S_5 are 1,1,4,4,5,5,6.
PROG
(Sage)
def A003040(n):
res = 1
for P in Partitions(n):
res = max(res, P.dimension())
return res
# Eric M. Schmidt, May 07 2013
CROSSREFS
A117500 gives the corresponding partitions of n.
Sequence in context: A342027 A343197 A030753 * A126317 A079437 A061220
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised and extended by N. J. A. Sloane, Apr 28 2006
a(29) corrected by Eric M. Schmidt, May 07 2013
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)