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A117500 Triangle read by rows in which row n gives the partition of n associated with highest degree representation of symmetric group S_n. 1
1, 2, 2, 1, 3, 1, 3, 1, 1, 3, 2, 1, 4, 2, 1, 4, 2, 1, 1, 4, 3, 1, 1, 4, 3, 2, 1, 5, 3, 2, 1, 5, 3, 2, 1, 1, 5, 4, 2, 1, 1, 6, 4, 2, 1, 1, 5, 4, 3, 2, 1, 6, 4, 3, 2, 1, 6, 4, 3, 2, 1, 1, 7, 4, 3, 2, 1, 1, 7, 5, 3, 2, 1, 1, 7, 5, 3, 2, 2, 1, 7, 5, 3, 2, 2, 1, 1, 7, 5, 4, 3, 2, 1, 7, 5, 4, 3, 2, 1 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

Note that a partition and its conjugate give the same degree representation of the symmetric group. We take the lexicographically earlier of the two.

REFERENCES

J. McKay, The largest degrees of irreducible characters of the symmetric group. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 terms.)

LINKS

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

FORMULA

If p_1 >= p_2 >= ... >= p_k is the partition of n, the degree of the representation (given in A003040) is n! * Product_{i<j} (b_i - b_j) / Product_i (b_i!), where b_i = p_i+k-i.

EXAMPLE

Triangle begins:

1

2

2 1

3 1

3 1 1

3 2 1

4 2 1

4 2 1 1

4 3 1 1

4 3 2 1

5 3 2 1

5 3 2 1 1

5 4 2 1 1

6 4 2 1 1

5 4 3 2 1

6 4 3 2 1

6 4 3 2 1 1

7 4 3 2 1 1

7 5 3 2 1 1

7 5 3 2 2 1

7 5 3 2 2 1 1

7 5 4 3 2 1

7 5 4 3 2 1 1

8 5 4 3 2 1 1

8 6 4 3 2 1 1

CROSSREFS

See A003040 for much more information. Cf. A060240.

Sequence in context: A166363 A117470 A070786 * A175245 A167413 A174167

Adjacent sequences:  A117497 A117498 A117499 * A117501 A117502 A117503

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Apr 28 2006

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Last modified February 15 04:59 EST 2012. Contains 205694 sequences.