{{{id=1|
# replace /home/tom/maths/full_group/ with the path to mult_functions.sage on your computer
load "/home/tom/maths/full_group/mult_functions.sage"
///
}}}

{{{id=2|
#prints multiplicity of rep p of S_N in kappa of U(N), or the mult of p\times kappa in (V_\nat)^n
N=6
kappa=[2,1]
for p in Partitions(N):
    print super_multiplicity("nat",p,kappa),p
///
1 [6]
3 [5, 1]
2 [4, 2]
2 [4, 1, 1]
0 [3, 3]
1 [3, 2, 1]
0 [3, 1, 1, 1]
0 [2, 2, 2]
0 [2, 2, 1, 1]
0 [2, 1, 1, 1, 1]
0 [1, 1, 1, 1, 1, 1]
}}}