A060369 a(n) is the maximum number of occurrences of a degree in the sequence of the degrees of the irreducible representations of the symmetric group S_n.

1, 2, 2, 2, 2, 4, 4, 2, 3, 2, 4, 4, 6, 6, 6, 4, 8, 6, 10, 6, 8, 8, 12, 8, 12, 12, 10, 12, 22, 14, 12, 12, 16, 18, 30, 14, 20, 26, 16, 20, 22, 20, 26, 25, 24, 24, 32, 16, 32, 30, 26, 24, 32, 32, 40, 32, 34, 32, 32, 34, 44, 30, 44, 36, 52, 34, 54, 38, 56, 50

Offset: 1

Author

Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001

Keywords

• nonn

Examples

			a(6) = 4 because the degrees for S_6 are 1,1,5,5,5,5,9,9,10,10,16 and the number 5 appears 4 times.
		

Programs

Mathematica

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]], If[i < 1, 0, Flatten@ Table[g[n - i*j, i - 1, Join[l, Array[i&, j]]], {j, 0, n/i}]]];
a[n_] := a[n] = If[n == 1, 1, MaximalBy[Tally[g[n, n, {}]], Last][[1, 2]]];
Table[Print[n, " ", a[n]];
a[n], {n, 1, 50}] (* Jean-François Alcover, Sep 23 2024, after Alois P. Heinz in A060240 *)

Sage

def A060369(n) :
    mult = {}
    for P in Partitions(n):
        dim = P.dimension()
        mult[dim] = mult.get(dim, 0) + 1
    return max(mult.values())
# Eric M. Schmidt, May 01 2013

Extensions

More terms from Eric M. Schmidt, May 01 2013