A003876 Degrees of irreducible representations of symmetric group S_12.

1, 1, 11, 11, 54, 54, 55, 55, 132, 132, 154, 154, 165, 165, 275, 275, 297, 297, 320, 320, 330, 330, 462, 462, 462, 462, 616, 616, 891, 891, 945, 945, 1155, 1155, 1320, 1320, 1408, 1408, 1485, 1485, 1650, 1650, 1728, 1728, 1925, 1925, 1925, 1925, 2079, 2079, 2100, 2112, 2112, 2376, 2376, 2640, 2673, 2673, 2970, 2970, 3080, 3080, 3520, 3520, 3564, 3564, 3696, 3696, 4158, 4158, 4455, 4455, 5632, 5632, 5775, 5775, 7700

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

All 77 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=12 of A060240.

Programs

GAP

A003876 := List(Irr(CharacterTable("S12")), chi->chi[1]);; Sort(A003876); # 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[12]] (* Jean-François Alcover, Sep 23 2024, after Alois P. Heinz in A060240 *)