A003872 Degrees of irreducible representations of symmetric group S_8.

1, 1, 7, 7, 14, 14, 20, 20, 21, 21, 28, 28, 35, 35, 42, 56, 56, 64, 64, 70, 70, 90

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

All 22 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=8 of A060240.

Programs

GAP

A003872 := List(Irr(CharacterTable("S8")), chi->chi[1]);; Sort(A003872); # Eric M. Schmidt, Jul 18 2012

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[8]] (* Jean-François Alcover, Sep 22 2024, after Alois P. Heinz in A060240 *)