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Identifier
Values
=>
Cc0002;cc-rep
[2]=>0 [1,1]=>0 [3]=>0 [2,1]=>1 [1,1,1]=>0 [4]=>1 [3,1]=>2 [2,2]=>0 [2,1,1]=>1 [1,1,1,1]=>0 [5]=>2 [4,1]=>3 [3,2]=>1 [3,1,1]=>1 [2,2,1]=>2 [2,1,1,1]=>1 [1,1,1,1,1]=>0 [6]=>5 [5,1]=>6 [4,2]=>3 [4,1,1]=>3 [3,3]=>2 [3,2,1]=>5 [3,1,1,1]=>2 [2,2,2]=>1 [2,2,1,1]=>1 [2,1,1,1,1]=>1 [1,1,1,1,1,1]=>0 [7]=>8 [6,1]=>9 [5,2]=>5 [5,1,1]=>5 [4,3]=>3 [4,2,1]=>7 [4,1,1,1]=>3 [3,3,1]=>6 [3,2,2]=>0 [3,2,1,1]=>3 [3,1,1,1,1]=>0 [2,2,2,1]=>5 [2,2,1,1,1]=>0 [2,1,1,1,1,1]=>1 [1,1,1,1,1,1,1]=>0 [8]=>14 [7,1]=>15 [6,2]=>10 [6,1,1]=>10 [5,3]=>7 [5,2,1]=>12 [5,1,1,1]=>7 [4,4]=>8 [4,3,1]=>10 [4,2,2]=>8 [4,2,1,1]=>12 [4,1,1,1,1]=>6 [3,3,2]=>4 [3,3,1,1]=>4 [3,2,2,1]=>7 [3,2,1,1,1]=>4 [3,1,1,1,1,1]=>1 [2,2,2,2]=>2 [2,2,2,1,1]=>6 [2,2,1,1,1,1]=>4 [2,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1]=>0 [9]=>21 [8,1]=>22 [7,2]=>16 [7,1,1]=>16 [6,3]=>12 [6,2,1]=>18 [6,1,1,1]=>12 [5,4]=>10 [5,3,1]=>15 [5,2,2]=>5 [5,2,1,1]=>10 [5,1,1,1,1]=>5 [4,4,1]=>16 [4,3,2]=>12 [4,3,1,1]=>12 [4,2,2,1]=>16 [4,2,1,1,1]=>12 [4,1,1,1,1,1]=>6 [3,3,3]=>8 [3,3,2,1]=>12 [3,3,1,1,1]=>13 [3,2,2,2]=>4 [3,2,2,1,1]=>6 [3,2,1,1,1,1]=>4 [3,1,1,1,1,1,1]=>6 [2,2,2,2,1]=>10 [2,2,2,1,1,1]=>4 [2,2,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1]=>0 [10]=>32 [9,1]=>33 [8,2]=>26 [8,1,1]=>26 [7,3]=>21 [7,2,1]=>28 [7,1,1,1]=>21 [6,4]=>18 [6,3,1]=>24 [6,2,2]=>12 [6,2,1,1]=>18 [6,1,1,1,1]=>12 [5,5]=>22 [5,4,1]=>22 [5,3,2]=>18 [5,3,1,1]=>18 [5,2,2,1]=>17 [5,2,1,1,1]=>16 [5,1,1,1,1,1]=>12 [4,4,2]=>14 [4,4,1,1]=>14 [4,3,3]=>6 [4,3,2,1]=>18 [4,3,1,1,1]=>6 [4,2,2,2]=>10 [4,2,2,1,1]=>14 [4,2,1,1,1,1]=>10 [4,1,1,1,1,1,1]=>2 [3,3,3,1]=>20 [3,3,2,2]=>7 [3,3,2,1,1]=>6 [3,3,1,1,1,1]=>7 [3,2,2,2,1]=>12 [3,2,2,1,1,1]=>7 [3,2,1,1,1,1,1]=>4 [3,1,1,1,1,1,1,1]=>6 [2,2,2,2,2]=>6 [2,2,2,2,1,1]=>6 [2,2,2,1,1,1,1]=>10 [2,2,1,1,1,1,1,1]=>5 [2,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1]=>0 [11]=>45 [10,1]=>46 [9,2]=>38 [9,1,1]=>38 [8,3]=>32 [8,2,1]=>40 [8,1,1,1]=>32 [7,4]=>28 [7,3,1]=>35 [7,2,2]=>21 [7,2,1,1]=>28 [7,1,1,1,1]=>21 [6,5]=>26 [6,4,1]=>32 [6,3,2]=>20 [6,3,1,1]=>20 [6,2,2,1]=>26 [6,2,1,1,1]=>20 [6,1,1,1,1,1]=>14 [5,5,1]=>36 [5,4,2]=>22 [5,4,1,1]=>22 [5,3,3]=>11 [5,3,2,1]=>26 [5,3,1,1,1]=>11 [5,2,2,2]=>10 [5,2,2,1,1]=>12 [5,2,1,1,1,1]=>10 [5,1,1,1,1,1,1]=>6 [4,4,3]=>14 [4,4,2,1]=>28 [4,4,1,1,1]=>14 [4,3,3,1]=>20 [4,3,2,2]=>14 [4,3,2,1,1]=>26 [4,3,1,1,1,1]=>8 [4,2,2,2,1]=>24 [4,2,2,1,1,1]=>14 [4,2,1,1,1,1,1]=>14 [4,1,1,1,1,1,1,1]=>4 [3,3,3,2]=>12 [3,3,3,1,1]=>12 [3,3,2,2,1]=>11 [3,3,2,1,1,1]=>22 [3,3,1,1,1,1,1]=>5 [3,2,2,2,2]=>0 [3,2,2,2,1,1]=>8 [3,2,2,1,1,1,1]=>2 [3,2,1,1,1,1,1,1]=>10 [3,1,1,1,1,1,1,1,1]=>0 [2,2,2,2,2,1]=>20 [2,2,2,2,1,1,1]=>0 [2,2,2,1,1,1,1,1]=>4 [2,2,1,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1,1]=>0 [12]=>65 [11,1]=>66 [10,2]=>57 [10,1,1]=>57 [9,3]=>50 [9,2,1]=>59 [9,1,1,1]=>50 [8,4]=>45 [8,3,1]=>53 [8,2,2]=>37 [8,2,1,1]=>45 [8,1,1,1,1]=>37 [7,5]=>42 [7,4,1]=>49 [7,3,2]=>35 [7,3,1,1]=>35 [7,2,2,1]=>42 [7,2,1,1,1]=>35 [7,1,1,1,1,1]=>28 [6,6]=>50 [6,5,1]=>47 [6,4,2]=>35 [6,4,1,1]=>35 [6,3,3]=>41 [6,3,2,1]=>47 [6,3,1,1,1]=>37 [6,2,2,2]=>26 [6,2,2,1,1]=>31 [6,2,1,1,1,1]=>26 [6,1,1,1,1,1,1]=>23 [5,5,2]=>37 [5,5,1,1]=>37 [5,4,3]=>29 [5,4,2,1]=>37 [5,4,1,1,1]=>25 [5,3,3,1]=>32 [5,3,2,2]=>18 [5,3,2,1,1]=>29 [5,3,1,1,1,1]=>14 [5,2,2,2,1]=>27 [5,2,2,1,1,1]=>16 [5,2,1,1,1,1,1]=>17 [5,1,1,1,1,1,1,1]=>12 [4,4,4]=>37 [4,4,3,1]=>35 [4,4,2,2]=>23 [4,4,2,1,1]=>37 [4,4,1,1,1,1]=>23 [4,3,3,2]=>19 [4,3,3,1,1]=>19 [4,3,2,2,1]=>39 [4,3,2,1,1,1]=>23 [4,3,1,1,1,1,1]=>15 [4,2,2,2,2]=>19 [4,2,2,2,1,1]=>19 [4,2,2,1,1,1,1]=>27 [4,2,1,1,1,1,1,1]=>11 [4,1,1,1,1,1,1,1,1]=>9 [3,3,3,3]=>26 [3,3,3,2,1]=>37 [3,3,3,1,1,1]=>26 [3,3,2,2,2]=>13 [3,3,2,2,1,1]=>12 [3,3,2,1,1,1,1]=>17 [3,3,1,1,1,1,1,1]=>8 [3,2,2,2,2,1]=>22 [3,2,2,2,1,1,1]=>17 [3,2,2,1,1,1,1,1]=>8 [3,2,1,1,1,1,1,1,1]=>15 [3,1,1,1,1,1,1,1,1,1]=>2 [2,2,2,2,2,2]=>12 [2,2,2,2,2,1,1]=>21 [2,2,2,2,1,1,1,1]=>12 [2,2,2,1,1,1,1,1,1]=>7 [2,2,1,1,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1,1,1]=>3 [1,1,1,1,1,1,1,1,1,1,1,1]=>0
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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