{{{id=2|
# replace /home/tom/maths/free_sigma/ with the path to cutjoin.sage on your computer
load "/home/tom/maths/free_sigma/cutjoin.sage"
///
}}}

{{{id=1|
# Compute the action of \S_{[2]} on the single trace \ket{n}

n=6

results=[]
number=[]

for p in permsOfType([2],n):
    temp = (p*genSingle(n)).cycle_type()
    if temp not in results:
        results.append(temp)
        number.append(1)
    else:
        number[results.index(temp)]+=1

for i in range(0,len(results)):    
    print number[i], results[i]
///
6 [5, 1]
6 [4, 2]
3 [3, 3]
}}}

{{{id=3|
# Compute the action of \S_{[2,2]} on the single trace \ket{n}

n=9

results=[]
number=[]

for p in permsOfType([2,2],n):
    temp = (p*genSingle(n)).cycle_type()
    if temp not in results:
        results.append(temp)
        number.append(1)
    else:
        number[results.index(temp)]+=1

for i in range(0,len(results)):    
    print number[i], results[i]
///
27 [7, 1, 1]
126 [9]
54 [6, 2, 1]
54 [5, 3, 1]
27 [5, 2, 2]
27 [4, 4, 1]
54 [4, 3, 2]
9 [3, 3, 3]
}}}