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... => 0
[4] generating graphics... => 1
[3,1] generating graphics... => 2
[2,2] generating graphics... => 0
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 0
[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... => 2
[2,1,1,1] generating graphics... => 1
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 5
[5,1] generating graphics... => 6
[4,2] generating graphics... => 3
[4,1,1] generating graphics... => 3
[3,3] generating graphics... => 2
[3,2,1] generating graphics... => 5
[3,1,1,1] generating graphics... => 2
[2,2,2] generating graphics... => 1
[2,2,1,1] generating graphics... => 1
[2,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1] generating graphics... => 0
[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... => 3
[3,3,1] generating graphics... => 6
[3,2,2] generating graphics... => 0
[3,2,1,1] generating graphics... => 3
[3,1,1,1,1] generating graphics... => 0
[2,2,2,1] generating graphics... => 5
[2,2,1,1,1] generating graphics... => 0
[2,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1] generating graphics... => 0
[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... => 7
[4,4] generating graphics... => 8
[4,3,1] generating graphics... => 10
[4,2,2] generating graphics... => 8
[4,2,1,1] generating graphics... => 12
[4,1,1,1,1] generating graphics... => 6
[3,3,2] generating graphics... => 4
[3,3,1,1] generating graphics... => 4
[3,2,2,1] generating graphics... => 7
[3,2,1,1,1] generating graphics... => 4
[3,1,1,1,1,1] generating graphics... => 1
[2,2,2,2] generating graphics... => 2
[2,2,2,1,1] generating graphics... => 6
[2,2,1,1,1,1] generating graphics... => 4
[2,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1] generating graphics... => 0
[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... => 12
[5,4] generating graphics... => 10
[5,3,1] generating graphics... => 15
[5,2,2] generating graphics... => 5
[5,2,1,1] generating graphics... => 10
[5,1,1,1,1] generating graphics... => 5
[4,4,1] generating graphics... => 16
[4,3,2] generating graphics... => 12
[4,3,1,1] generating graphics... => 12
[4,2,2,1] generating graphics... => 16
[4,2,1,1,1] generating graphics... => 12
[4,1,1,1,1,1] generating graphics... => 6
[3,3,3] generating graphics... => 8
[3,3,2,1] generating graphics... => 12
[3,3,1,1,1] generating graphics... => 13
[3,2,2,2] generating graphics... => 4
[3,2,2,1,1] generating graphics... => 6
[3,2,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1] generating graphics... => 6
[2,2,2,2,1] generating graphics... => 10
[2,2,2,1,1,1] generating graphics... => 4
[2,2,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1] generating graphics... => 0
[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... => 21
[6,4] generating graphics... => 18
[6,3,1] generating graphics... => 24
[6,2,2] generating graphics... => 12
[6,2,1,1] generating graphics... => 18
[6,1,1,1,1] generating graphics... => 12
[5,5] generating graphics... => 22
[5,4,1] generating graphics... => 22
[5,3,2] generating graphics... => 18
[5,3,1,1] generating graphics... => 18
[5,2,2,1] generating graphics... => 17
[5,2,1,1,1] generating graphics... => 16
[5,1,1,1,1,1] generating graphics... => 12
[4,4,2] generating graphics... => 14
[4,4,1,1] generating graphics... => 14
[4,3,3] generating graphics... => 6
[4,3,2,1] generating graphics... => 18
[4,3,1,1,1] generating graphics... => 6
[4,2,2,2] generating graphics... => 10
[4,2,2,1,1] generating graphics... => 14
[4,2,1,1,1,1] generating graphics... => 10
[4,1,1,1,1,1,1] generating graphics... => 2
[3,3,3,1] generating graphics... => 20
[3,3,2,2] generating graphics... => 7
[3,3,2,1,1] generating graphics... => 6
[3,3,1,1,1,1] generating graphics... => 7
[3,2,2,2,1] generating graphics... => 12
[3,2,2,1,1,1] generating graphics... => 7
[3,2,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1] generating graphics... => 6
[2,2,2,2,2] generating graphics... => 6
[2,2,2,2,1,1] generating graphics... => 6
[2,2,2,1,1,1,1] generating graphics... => 10
[2,2,1,1,1,1,1,1] generating graphics... => 5
[2,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[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... => 32
[7,4] generating graphics... => 28
[7,3,1] generating graphics... => 35
[7,2,2] generating graphics... => 21
[7,2,1,1] generating graphics... => 28
[7,1,1,1,1] generating graphics... => 21
[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... => 26
[6,2,1,1,1] generating graphics... => 20
[6,1,1,1,1,1] generating graphics... => 14
[5,5,1] generating graphics... => 36
[5,4,2] generating graphics... => 22
[5,4,1,1] generating graphics... => 22
[5,3,3] generating graphics... => 11
[5,3,2,1] generating graphics... => 26
[5,3,1,1,1] generating graphics... => 11
[5,2,2,2] generating graphics... => 10
[5,2,2,1,1] generating graphics... => 12
[5,2,1,1,1,1] generating graphics... => 10
[5,1,1,1,1,1,1] generating graphics... => 6
[4,4,3] generating graphics... => 14
[4,4,2,1] generating graphics... => 28
[4,4,1,1,1] generating graphics... => 14
[4,3,3,1] generating graphics... => 20
[4,3,2,2] generating graphics... => 14
[4,3,2,1,1] generating graphics... => 26
[4,3,1,1,1,1] generating graphics... => 8
[4,2,2,2,1] generating graphics... => 24
[4,2,2,1,1,1] generating graphics... => 14
[4,2,1,1,1,1,1] generating graphics... => 14
[4,1,1,1,1,1,1,1] generating graphics... => 4
[3,3,3,2] generating graphics... => 12
[3,3,3,1,1] generating graphics... => 12
[3,3,2,2,1] generating graphics... => 11
[3,3,2,1,1,1] generating graphics... => 22
[3,3,1,1,1,1,1] generating graphics... => 5
[3,2,2,2,2] generating graphics... => 0
[3,2,2,2,1,1] generating graphics... => 8
[3,2,2,1,1,1,1] generating graphics... => 2
[3,2,1,1,1,1,1,1] generating graphics... => 10
[3,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,1] generating graphics... => 20
[2,2,2,2,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1] generating graphics... => 4
[2,2,1,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[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... => 50
[8,4] generating graphics... => 45
[8,3,1] generating graphics... => 53
[8,2,2] generating graphics... => 37
[8,2,1,1] generating graphics... => 45
[8,1,1,1,1] generating graphics... => 37
[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... => 42
[7,2,1,1,1] generating graphics... => 35
[7,1,1,1,1,1] generating graphics... => 28
[6,6] generating graphics... => 50
[6,5,1] generating graphics... => 47
[6,4,2] generating graphics... => 35
[6,4,1,1] generating graphics... => 35
[6,3,3] generating graphics... => 41
[6,3,2,1] generating graphics... => 47
[6,3,1,1,1] generating graphics... => 37
[6,2,2,2] generating graphics... => 26
[6,2,2,1,1] generating graphics... => 31
[6,2,1,1,1,1] generating graphics... => 26
[6,1,1,1,1,1,1] generating graphics... => 23
[5,5,2] generating graphics... => 37
[5,5,1,1] generating graphics... => 37
[5,4,3] generating graphics... => 29
[5,4,2,1] generating graphics... => 37
[5,4,1,1,1] generating graphics... => 25
[5,3,3,1] generating graphics... => 32
[5,3,2,2] generating graphics... => 18
[5,3,2,1,1] generating graphics... => 29
[5,3,1,1,1,1] generating graphics... => 14
[5,2,2,2,1] generating graphics... => 27
[5,2,2,1,1,1] generating graphics... => 16
[5,2,1,1,1,1,1] generating graphics... => 17
[5,1,1,1,1,1,1,1] generating graphics... => 12
[4,4,4] generating graphics... => 37
[4,4,3,1] generating graphics... => 35
[4,4,2,2] generating graphics... => 23
[4,4,2,1,1] generating graphics... => 37
[4,4,1,1,1,1] generating graphics... => 23
[4,3,3,2] generating graphics... => 19
[4,3,3,1,1] generating graphics... => 19
[4,3,2,2,1] generating graphics... => 39
[4,3,2,1,1,1] generating graphics... => 23
[4,3,1,1,1,1,1] generating graphics... => 15
[4,2,2,2,2] generating graphics... => 19
[4,2,2,2,1,1] generating graphics... => 19
[4,2,2,1,1,1,1] generating graphics... => 27
[4,2,1,1,1,1,1,1] generating graphics... => 11
[4,1,1,1,1,1,1,1,1] generating graphics... => 9
[3,3,3,3] generating graphics... => 26
[3,3,3,2,1] generating graphics... => 37
[3,3,3,1,1,1] generating graphics... => 26
[3,3,2,2,2] generating graphics... => 13
[3,3,2,2,1,1] generating graphics... => 12
[3,3,2,1,1,1,1] generating graphics... => 17
[3,3,1,1,1,1,1,1] generating graphics... => 8
[3,2,2,2,2,1] generating graphics... => 22
[3,2,2,2,1,1,1] generating graphics... => 17
[3,2,2,1,1,1,1,1] generating graphics... => 8
[3,2,1,1,1,1,1,1,1] generating graphics... => 15
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2,2] generating graphics... => 12
[2,2,2,2,2,1,1] generating graphics... => 21
[2,2,2,2,1,1,1,1] generating graphics... => 12
[2,2,2,1,1,1,1,1,1] generating graphics... => 7
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
click to show generating function       
Description
The number of characters of the symmetric group whose value on the partition is zero.
The maximal value for any given size is recorded in [2].
References
[1] Miller, A. R. Note on parity and the irreducible characters of the symmetric group arXiv:1708.03267
[2] Maximal number of zeros in a column of the character table of the symmetric group S_n. OEIS:A086642
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 13:44 by Martin Rubey