cp's OEIS Frontend

A117500 Triangle read by rows in which row n gives the partition of n associated with highest degree representation of symmetric group S_n.

%I A117500 #12 Oct 01 2015 18:17:43
%S A117500 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,
%T A117500 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,
%U A117500 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
%N A117500 Triangle read by rows in which row n gives the partition of n associated with highest degree representation of symmetric group S_n.
%C A117500 Note that a partition and its conjugate give the same degree representation of the symmetric group. We take the lexicographically earlier of the two.
%H A117500 J. McKay, <a href="http://dx.doi.org/10.1090/S0025-5718-1976-0404414-X">The largest degrees of irreducible characters of the symmetric group</a>. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 rows on pp. 627-629.)
%H A117500 J. McKay, <a href="/A003040/a003040a.jpg">Page 1 of 5 pages of tables from Math. Comp. paper</a>
%H A117500 J. McKay, <a href="/A003040/a003040b.jpg">Page 2 of 5 pages of tables from Math. Comp. paper</a>
%H A117500 J. McKay, <a href="/A003040/a003040c.jpg">Page 3 of 5 pages of tables from Math. Comp. paper</a>
%H A117500 J. McKay, <a href="/A003040/a003040d.jpg">Page 4 of 5 pages of tables from Math. Comp. paper</a>
%H A117500 J. McKay, <a href="/A003040/a003040e.jpg">Page 5 of 5 pages of tables from Math. Comp. paper</a>
%F A117500 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.
%e A117500 Triangle begins:
%e A117500 1
%e A117500 2
%e A117500 2 1
%e A117500 3 1
%e A117500 3 1 1
%e A117500 3 2 1
%e A117500 4 2 1
%e A117500 4 2 1 1
%e A117500 4 3 1 1
%e A117500 4 3 2 1
%e A117500 5 3 2 1
%e A117500 5 3 2 1 1
%e A117500 5 4 2 1 1
%e A117500 6 4 2 1 1
%e A117500 5 4 3 2 1
%e A117500 6 4 3 2 1
%e A117500 6 4 3 2 1 1
%e A117500 7 4 3 2 1 1
%e A117500 7 5 3 2 1 1
%e A117500 7 5 3 2 2 1
%e A117500 7 5 3 2 2 1 1
%e A117500 7 5 4 3 2 1
%e A117500 7 5 4 3 2 1 1
%e A117500 8 5 4 3 2 1 1
%e A117500 8 6 4 3 2 1 1
%Y A117500 See A003040 for much more information. Cf. A060240.
%K A117500 nonn,tabf
%O A117500 1,2
%A A117500 _N. J. A. Sloane_, Apr 28 2006