A003869 Degrees of irreducible representations of symmetric group S_5.

1, 1, 4, 4, 5, 5, 6

Offset

1,3

Comments

All 7 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..7.

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

Prog

(Magma) // See A003875 for Magma code
(GAP) A003869 := List(Irr(CharacterTable("S5")), chi->chi[1]);; Sort(A003869); # Eric M. Schmidt, Jul 18 2012

Crossrefs

Row n=5 of A060240.

Cf. A003870, A003871, A003872, A003873.

Sequence in context: A332609 A244234 A237449 * A386290 A065864 A120205

Adjacent sequences: A003866 A003867 A003868 * A003870 A003871 A003872

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved