1,2

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

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

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

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.

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

See A003040 for much more information. Cf. A060240.

Sequence in context: A166363 A117470 A070786 this_sequence A167413 A159876 A044924

Adjacent sequences: A117497 A117498 A117499 this_sequence A117501 A117502 A117503

nonn,tabf

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