A059796 Degrees of irreducible representations of symmetric group S_14.

1, 1, 13, 13, 77, 77, 78, 78, 273, 273, 286, 286, 429, 429, 560, 560, 637, 637, 715, 715, 1001, 1001, 1001, 1001, 1287, 1287, 1365, 1365, 1716, 1716, 2002, 2002, 2079, 2079, 4368, 4368, 4576, 4576, 4928, 4928, 5733, 5733, 6006, 6006, 6006, 6006, 6006, 6006, 6435

Offset: 1

Author

N. J. A. Sloane, Feb 22 2001

Keywords

• nonn
• fini
• full

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

• Eric M. Schmidt, Table of n, a(n) for n = 1..135 (complete sequence)

Crossrefs

Cf. A003869 - A003877.

Row n=14 of A060240.

Programs

GAP

List(Irr(CharacterTable("S14")), chi->chi[1]); # Eric M. Schmidt, Jul 18 2012

Magma

// See A003875 for MAGMA code.

Maple

h:= proc(l) local n; n:= nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
      add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), `if`(i<1, 0,
                 seq(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
sort([g(14$2, [])])[];  # Alois P. Heinz, Sep 23 2024

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[14]] (* Jean-François Alcover, Sep 23 2024, after Alois P. Heinz *)