Identifier
Identifier
Values
[2] generating graphics... => 0
[1,1] generating graphics... => 0
[3] generating graphics... => 0
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 1
[4] generating graphics... => 1
[3,1] generating graphics... => 2
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 2
[4,1] generating graphics... => 3
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 1
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 3
[1,1,1,1,1] generating graphics... => 3
[6] generating graphics... => 5
[5,1] generating graphics... => 6
[4,2] generating graphics... => 3
[4,1,1] generating graphics... => 3
[3,3] generating graphics... => 5
[3,2,1] generating graphics... => 5
[3,1,1,1] generating graphics... => 5
[2,2,2] generating graphics... => 3
[2,2,1,1] generating graphics... => 3
[2,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1] generating graphics... => 3
[7] generating graphics... => 8
[6,1] generating graphics... => 9
[5,2] generating graphics... => 5
[5,1,1] generating graphics... => 5
[4,3] generating graphics... => 3
[4,2,1] generating graphics... => 7
[4,1,1,1] generating graphics... => 7
[3,3,1] generating graphics... => 9
[3,2,2] generating graphics... => 3
[3,2,1,1] generating graphics... => 3
[3,1,1,1,1] generating graphics... => 3
[2,2,2,1] generating graphics... => 7
[2,2,1,1,1] generating graphics... => 7
[2,1,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1,1] generating graphics... => 7
[8] generating graphics... => 14
[7,1] generating graphics... => 15
[6,2] generating graphics... => 10
[6,1,1] generating graphics... => 10
[5,3] generating graphics... => 7
[5,2,1] generating graphics... => 12
[5,1,1,1] generating graphics... => 12
[4,4] generating graphics... => 14
[4,3,1] generating graphics... => 10
[4,2,2] generating graphics... => 14
[4,2,1,1] generating graphics... => 14
[4,1,1,1,1] generating graphics... => 14
[3,3,2] generating graphics... => 10
[3,3,1,1] generating graphics... => 10
[3,2,2,1] generating graphics... => 10
[3,2,1,1,1] generating graphics... => 10
[3,1,1,1,1,1] generating graphics... => 10
[2,2,2,2] generating graphics... => 14
[2,2,2,1,1] generating graphics... => 14
[2,2,1,1,1,1] generating graphics... => 14
[2,1,1,1,1,1,1] generating graphics... => 14
[1,1,1,1,1,1,1,1] generating graphics... => 14
[9] generating graphics... => 21
[8,1] generating graphics... => 22
[7,2] generating graphics... => 16
[7,1,1] generating graphics... => 16
[6,3] generating graphics... => 12
[6,2,1] generating graphics... => 18
[6,1,1,1] generating graphics... => 18
[5,4] generating graphics... => 10
[5,3,1] generating graphics... => 15
[5,2,2] generating graphics... => 10
[5,2,1,1] generating graphics... => 10
[5,1,1,1,1] generating graphics... => 10
[4,4,1] generating graphics... => 22
[4,3,2] generating graphics... => 14
[4,3,1,1] generating graphics... => 14
[4,2,2,1] generating graphics... => 22
[4,2,1,1,1] generating graphics... => 22
[4,1,1,1,1,1] generating graphics... => 22
[3,3,3] generating graphics... => 12
[3,3,2,1] generating graphics... => 18
[3,3,1,1,1] generating graphics... => 18
[3,2,2,2] generating graphics... => 14
[3,2,2,1,1] generating graphics... => 14
[3,2,1,1,1,1] generating graphics... => 14
[3,1,1,1,1,1,1] generating graphics... => 14
[2,2,2,2,1] generating graphics... => 22
[2,2,2,1,1,1] generating graphics... => 22
[2,2,1,1,1,1,1] generating graphics... => 22
[2,1,1,1,1,1,1,1] generating graphics... => 22
[1,1,1,1,1,1,1,1,1] generating graphics... => 22
[10] generating graphics... => 32
[9,1] generating graphics... => 33
[8,2] generating graphics... => 26
[8,1,1] generating graphics... => 26
[7,3] generating graphics... => 21
[7,2,1] generating graphics... => 28
[7,1,1,1] generating graphics... => 28
[6,4] generating graphics... => 18
[6,3,1] generating graphics... => 24
[6,2,2] generating graphics... => 18
[6,2,1,1] generating graphics... => 18
[6,1,1,1,1] generating graphics... => 18
[5,5] generating graphics... => 32
[5,4,1] generating graphics... => 22
[5,3,2] generating graphics... => 20
[5,3,1,1] generating graphics... => 20
[5,2,2,1] generating graphics... => 22
[5,2,1,1,1] generating graphics... => 22
[5,1,1,1,1,1] generating graphics... => 22
[4,4,2] generating graphics... => 26
[4,4,1,1] generating graphics... => 26
[4,3,3] generating graphics... => 18
[4,3,2,1] generating graphics... => 18
[4,3,1,1,1] generating graphics... => 18
[4,2,2,2] generating graphics... => 26
[4,2,2,1,1] generating graphics... => 26
[4,2,1,1,1,1] generating graphics... => 26
[4,1,1,1,1,1,1] generating graphics... => 26
[3,3,3,1] generating graphics... => 24
[3,3,2,2] generating graphics... => 18
[3,3,2,1,1] generating graphics... => 18
[3,3,1,1,1,1] generating graphics... => 18
[3,2,2,2,1] generating graphics... => 18
[3,2,2,1,1,1] generating graphics... => 18
[3,2,1,1,1,1,1] generating graphics... => 18
[3,1,1,1,1,1,1,1] generating graphics... => 18
[2,2,2,2,2] generating graphics... => 26
[2,2,2,2,1,1] generating graphics... => 26
[2,2,2,1,1,1,1] generating graphics... => 26
[2,2,1,1,1,1,1,1] generating graphics... => 26
[2,1,1,1,1,1,1,1,1] generating graphics... => 26
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 26
[11] generating graphics... => 45
[10,1] generating graphics... => 46
[9,2] generating graphics... => 38
[9,1,1] generating graphics... => 38
[8,3] generating graphics... => 32
[8,2,1] generating graphics... => 40
[8,1,1,1] generating graphics... => 40
[7,4] generating graphics... => 28
[7,3,1] generating graphics... => 35
[7,2,2] generating graphics... => 28
[7,2,1,1] generating graphics... => 28
[7,1,1,1,1] generating graphics... => 28
[6,5] generating graphics... => 26
[6,4,1] generating graphics... => 32
[6,3,2] generating graphics... => 20
[6,3,1,1] generating graphics... => 20
[6,2,2,1] generating graphics... => 32
[6,2,1,1,1] generating graphics... => 32
[6,1,1,1,1,1] generating graphics... => 32
[5,5,1] generating graphics... => 46
[5,4,2] generating graphics... => 24
[5,4,1,1] generating graphics... => 24
[5,3,3] generating graphics... => 26
[5,3,2,1] generating graphics... => 26
[5,3,1,1,1] generating graphics... => 26
[5,2,2,2] generating graphics... => 24
[5,2,2,1,1] generating graphics... => 24
[5,2,1,1,1,1] generating graphics... => 24
[5,1,1,1,1,1,1] generating graphics... => 24
[4,4,3] generating graphics... => 32
[4,4,2,1] generating graphics... => 40
[4,4,1,1,1] generating graphics... => 40
[4,3,3,1] generating graphics... => 32
[4,3,2,2] generating graphics... => 32
[4,3,2,1,1] generating graphics... => 32
[4,3,1,1,1,1] generating graphics... => 32
[4,2,2,2,1] generating graphics... => 40
[4,2,2,1,1,1] generating graphics... => 40
[4,2,1,1,1,1,1] generating graphics... => 40
[4,1,1,1,1,1,1,1] generating graphics... => 40
[3,3,3,2] generating graphics... => 20
[3,3,3,1,1] generating graphics... => 20
[3,3,2,2,1] generating graphics... => 32
[3,3,2,1,1,1] generating graphics... => 32
[3,3,1,1,1,1,1] generating graphics... => 32
[3,2,2,2,2] generating graphics... => 32
[3,2,2,2,1,1] generating graphics... => 32
[3,2,2,1,1,1,1] generating graphics... => 32
[3,2,1,1,1,1,1,1] generating graphics... => 32
[3,1,1,1,1,1,1,1,1] generating graphics... => 32
[2,2,2,2,2,1] generating graphics... => 40
[2,2,2,2,1,1,1] generating graphics... => 40
[2,2,2,1,1,1,1,1] generating graphics... => 40
[2,2,1,1,1,1,1,1,1] generating graphics... => 40
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 40
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 40
[12] generating graphics... => 65
[11,1] generating graphics... => 66
[10,2] generating graphics... => 57
[10,1,1] generating graphics... => 57
[9,3] generating graphics... => 50
[9,2,1] generating graphics... => 59
[9,1,1,1] generating graphics... => 59
[8,4] generating graphics... => 45
[8,3,1] generating graphics... => 53
[8,2,2] generating graphics... => 45
[8,2,1,1] generating graphics... => 45
[8,1,1,1,1] generating graphics... => 45
[7,5] generating graphics... => 42
[7,4,1] generating graphics... => 49
[7,3,2] generating graphics... => 35
[7,3,1,1] generating graphics... => 35
[7,2,2,1] generating graphics... => 49
[7,2,1,1,1] generating graphics... => 49
[7,1,1,1,1,1] generating graphics... => 49
[6,6] generating graphics... => 65
[6,5,1] generating graphics... => 47
[6,4,2] generating graphics... => 37
[6,4,1,1] generating graphics... => 37
[6,3,3] generating graphics... => 65
[6,3,2,1] generating graphics... => 49
[6,3,1,1,1] generating graphics... => 49
[6,2,2,2] generating graphics... => 37
[6,2,2,1,1] generating graphics... => 37
[6,2,1,1,1,1] generating graphics... => 37
[6,1,1,1,1,1,1] generating graphics... => 37
[5,5,2] generating graphics... => 57
[5,5,1,1] generating graphics... => 57
[5,4,3] generating graphics... => 33
[5,4,2,1] generating graphics... => 37
[5,4,1,1,1] generating graphics... => 37
[5,3,3,1] generating graphics... => 47
[5,3,2,2] generating graphics... => 33
[5,3,2,1,1] generating graphics... => 33
[5,3,1,1,1,1] generating graphics... => 33
[5,2,2,2,1] generating graphics... => 37
[5,2,2,1,1,1] generating graphics... => 37
[5,2,1,1,1,1,1] generating graphics... => 37
[5,1,1,1,1,1,1,1] generating graphics... => 37
[4,4,4] generating graphics... => 45
[4,4,3,1] generating graphics... => 53
[4,4,2,2] generating graphics... => 45
[4,4,2,1,1] generating graphics... => 45
[4,4,1,1,1,1] generating graphics... => 45
[4,3,3,2] generating graphics... => 37
[4,3,3,1,1] generating graphics... => 37
[4,3,2,2,1] generating graphics... => 53
[4,3,2,1,1,1] generating graphics... => 53
[4,3,1,1,1,1,1] generating graphics... => 53
[4,2,2,2,2] generating graphics... => 45
[4,2,2,2,1,1] generating graphics... => 45
[4,2,2,1,1,1,1] generating graphics... => 45
[4,2,1,1,1,1,1,1] generating graphics... => 45
[4,1,1,1,1,1,1,1,1] generating graphics... => 45
[3,3,3,3] generating graphics... => 65
[3,3,3,2,1] generating graphics... => 49
[3,3,3,1,1,1] generating graphics... => 49
[3,3,2,2,2] generating graphics... => 37
[3,3,2,2,1,1] generating graphics... => 37
[3,3,2,1,1,1,1] generating graphics... => 37
[3,3,1,1,1,1,1,1] generating graphics... => 37
[3,2,2,2,2,1] generating graphics... => 53
[3,2,2,2,1,1,1] generating graphics... => 53
[3,2,2,1,1,1,1,1] generating graphics... => 53
[3,2,1,1,1,1,1,1,1] generating graphics... => 53
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 53
[2,2,2,2,2,2] generating graphics... => 45
[2,2,2,2,2,1,1] generating graphics... => 45
[2,2,2,2,1,1,1,1] generating graphics... => 45
[2,2,2,1,1,1,1,1,1] generating graphics... => 45
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 45
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 45
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 45
click to show generating function       
Description
The number of characters of the symmetric group whose value on the partition is even.
References
[1] Miller, A. R. Note on parity and the irreducible characters of the symmetric group arXiv:1708.03267
Code
def statistic(la):
    s = SymmetricFunctions(ZZ).s()
    p = SymmetricFunctions(ZZ).p()
    P = Partitions(la.size())
    r = P.cardinality()
    res = [0]*r    
    for i, (mu, v) in enumerate(s(p(la))):
            res[i] = v
    return len([1 for e in res if is_even(e)])

Created
Aug 12, 2017 at 11:37 by Martin Rubey
Updated
Aug 12, 2017 at 11:37 by Martin Rubey