A003874 Degrees of irreducible representations of symmetric group S_10.

1, 1, 9, 9, 35, 35, 36, 36, 42, 42, 75, 75, 84, 84, 90, 90, 126, 126, 160, 160, 210, 210, 225, 225, 252, 252, 288, 288, 300, 300, 315, 315, 350, 350, 448, 450, 450, 525, 525, 567, 567, 768

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

All 42 terms of this finite sequence are shown.

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 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].

Crossrefs

Row n=10 of A060240.

Programs

GAP

A003874 := List(Irr(CharacterTable("S10")), chi->chi[1]);; Sort(A003874); # Eric M. Schmidt, Jul 18 2012

Magma

// See A003875 for Magma code.

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}]]];
T[n_] := g[n, n, {}];
Sort[T[10]] (* Jean-François Alcover, Sep 23 2024, after Alois P. Heinz in A060240 *)