A003870 Degrees of irreducible representations of symmetric group S_6.

1, 1, 5, 5, 5, 5, 9, 9, 10, 10, 16

Offset

1,3

Comments

All 11 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].

Links

Table of n, a(n) for n=1..11.

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

Prog

(Magma) CharacterTable(SymmetricGroup(6));
(GAP) A003870 := List(Irr(CharacterTable("S6")), chi->chi[1]);; Sort(A003870); # Eric M. Schmidt, Jul 18 2012

Crossrefs

Row n=6 of A060240.

Sequence in context: A033299 A293982 A071577 * A304681 A076407 A134701

Adjacent sequences: A003867 A003868 A003869 * A003871 A003872 A003873

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved