Identifier
Identifier
Values
[1] generating graphics... => 1
[2] generating graphics... => 1
[1,1] generating graphics... => 1
[3] generating graphics... => 1
[2,1] generating graphics... => 0
[1,1,1] generating graphics... => 1
[4] generating graphics... => 1
[3,1] generating graphics... => 1
[2,2] generating graphics... => 2
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 1
[4,1] generating graphics... => 0
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 2
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 0
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 1
[5,1] generating graphics... => 1
[4,2] generating graphics... => 3
[4,1,1] generating graphics... => 2
[3,3] generating graphics... => 3
[3,2,1] generating graphics... => 0
[3,1,1,1] generating graphics... => 2
[2,2,2] generating graphics... => 3
[2,2,1,1] generating graphics... => 3
[2,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 1
[6,1] generating graphics... => 0
[5,2] generating graphics... => 2
[5,1,1] generating graphics... => 3
[4,3] generating graphics... => 0
[4,2,1] generating graphics... => 1
[4,1,1,1] generating graphics... => 0
[3,3,1] generating graphics... => 3
[3,2,2] generating graphics... => 3
[3,2,1,1] generating graphics... => 1
[3,1,1,1,1] generating graphics... => 3
[2,2,2,1] generating graphics... => 0
[2,2,1,1,1] generating graphics... => 2
[2,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 1
[7,1] generating graphics... => 1
[6,2] generating graphics... => 4
[6,1,1] generating graphics... => 3
[5,3] generating graphics... => 4
[5,2,1] generating graphics... => 0
[5,1,1,1] generating graphics... => 3
[4,4] generating graphics... => 6
[4,3,1] generating graphics... => 2
[4,2,2] generating graphics... => 8
[4,2,1,1] generating graphics... => 6
[4,1,1,1,1] generating graphics... => 3
[3,3,2] generating graphics... => 6
[3,3,1,1] generating graphics... => 8
[3,2,2,1] generating graphics... => 2
[3,2,1,1,1] generating graphics... => 0
[3,1,1,1,1,1] generating graphics... => 3
[2,2,2,2] generating graphics... => 6
[2,2,2,1,1] generating graphics... => 4
[2,2,1,1,1,1] generating graphics... => 4
[2,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 1
[8,1] generating graphics... => 0
[7,2] generating graphics... => 3
[7,1,1] generating graphics... => 4
[6,3] generating graphics... => 0
[6,2,1] generating graphics... => 1
[6,1,1,1] generating graphics... => 0
[5,4] generating graphics... => 2
[5,3,1] generating graphics... => 6
[5,2,2] generating graphics... => 8
[5,2,1,1] generating graphics... => 3
[5,1,1,1,1] generating graphics... => 6
[4,4,1] generating graphics... => 4
[4,3,2] generating graphics... => 0
[4,3,1,1] generating graphics... => 0
[4,2,2,1] generating graphics... => 0
[4,2,1,1,1] generating graphics... => 3
[4,1,1,1,1,1] generating graphics... => 0
[3,3,3] generating graphics... => 6
[3,3,2,1] generating graphics... => 0
[3,3,1,1,1] generating graphics... => 8
[3,2,2,2] generating graphics... => 4
[3,2,2,1,1] generating graphics... => 6
[3,2,1,1,1,1] generating graphics... => 1
[3,1,1,1,1,1,1] generating graphics... => 4
[2,2,2,2,1] generating graphics... => 2
[2,2,2,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 1
[9,1] generating graphics... => 1
[8,2] generating graphics... => 5
[8,1,1] generating graphics... => 4
[7,3] generating graphics... => 5
[7,2,1] generating graphics... => 0
[7,1,1,1] generating graphics... => 4
[6,4] generating graphics... => 10
[6,3,1] generating graphics... => 5
[6,2,2] generating graphics... => 15
[6,2,1,1] generating graphics... => 10
[6,1,1,1,1] generating graphics... => 6
[5,5] generating graphics... => 10
[5,4,1] generating graphics... => 0
[5,3,2] generating graphics... => 10
[5,3,1,1] generating graphics... => 15
[5,2,2,1] generating graphics... => 5
[5,2,1,1,1] generating graphics... => 0
[5,1,1,1,1,1] generating graphics... => 6
[4,4,2] generating graphics... => 20
[4,4,1,1] generating graphics... => 20
[4,3,3] generating graphics... => 10
[4,3,2,1] generating graphics... => 0
[4,3,1,1,1] generating graphics... => 5
[4,2,2,2] generating graphics... => 20
[4,2,2,1,1] generating graphics... => 15
[4,2,1,1,1,1] generating graphics... => 10
[4,1,1,1,1,1,1] generating graphics... => 4
[3,3,3,1] generating graphics... => 10
[3,3,2,2] generating graphics... => 20
[3,3,2,1,1] generating graphics... => 10
[3,3,1,1,1,1] generating graphics... => 15
[3,2,2,2,1] generating graphics... => 0
[3,2,2,1,1,1] generating graphics... => 5
[3,2,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1] generating graphics... => 4
[2,2,2,2,2] generating graphics... => 10
[2,2,2,2,1,1] generating graphics... => 10
[2,2,2,1,1,1,1] generating graphics... => 5
[2,2,1,1,1,1,1,1] generating graphics... => 5
[2,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 1
[10,1] generating graphics... => 0
[9,2] generating graphics... => 4
[9,1,1] generating graphics... => 5
[8,3] generating graphics... => 0
[8,2,1] generating graphics... => 1
[8,1,1,1] generating graphics... => 0
[7,4] generating graphics... => 5
[7,3,1] generating graphics... => 10
[7,2,2] generating graphics... => 15
[7,2,1,1] generating graphics... => 6
[7,1,1,1,1] generating graphics... => 10
[6,5] generating graphics... => 0
[6,4,1] generating graphics... => 5
[6,3,2] generating graphics... => 0
[6,3,1,1] generating graphics... => 0
[6,2,2,1] generating graphics... => 0
[6,2,1,1,1] generating graphics... => 4
[6,1,1,1,1,1] generating graphics... => 0
[5,5,1] generating graphics... => 10
[5,4,2] generating graphics... => 10
[5,4,1,1] generating graphics... => 5
[5,3,3] generating graphics... => 20
[5,3,2,1] generating graphics... => 0
[5,3,1,1,1] generating graphics... => 20
[5,2,2,2] generating graphics... => 15
[5,2,2,1,1] generating graphics... => 20
[5,2,1,1,1,1] generating graphics... => 4
[5,1,1,1,1,1,1] generating graphics... => 10
[4,4,3] generating graphics... => 10
[4,4,2,1] generating graphics... => 0
[4,4,1,1,1] generating graphics... => 15
[4,3,3,1] generating graphics... => 0
[4,3,2,2] generating graphics... => 0
[4,3,2,1,1] generating graphics... => 0
[4,3,1,1,1,1] generating graphics... => 0
[4,2,2,2,1] generating graphics... => 5
[4,2,2,1,1,1] generating graphics... => 0
[4,2,1,1,1,1,1] generating graphics... => 6
[4,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,2] generating graphics... => 10
[3,3,3,1,1] generating graphics... => 20
[3,3,2,2,1] generating graphics... => 10
[3,3,2,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1] generating graphics... => 15
[3,2,2,2,2] generating graphics... => 10
[3,2,2,2,1,1] generating graphics... => 5
[3,2,2,1,1,1,1] generating graphics... => 10
[3,2,1,1,1,1,1,1] generating graphics... => 1
[3,1,1,1,1,1,1,1,1] generating graphics... => 5
[2,2,2,2,2,1] generating graphics... => 0
[2,2,2,2,1,1,1] generating graphics... => 5
[2,2,2,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1] generating graphics... => 4
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 1
[11,1] generating graphics... => 1
[10,2] generating graphics... => 6
[10,1,1] generating graphics... => 5
[9,3] generating graphics... => 6
[9,2,1] generating graphics... => 0
[9,1,1,1] generating graphics... => 5
[8,4] generating graphics... => 15
[8,3,1] generating graphics... => 9
[8,2,2] generating graphics... => 24
[8,2,1,1] generating graphics... => 15
[8,1,1,1,1] generating graphics... => 10
[7,5] generating graphics... => 15
[7,4,1] generating graphics... => 0
[7,3,2] generating graphics... => 15
[7,3,1,1] generating graphics... => 24
[7,2,2,1] generating graphics... => 9
[7,2,1,1,1] generating graphics... => 0
[7,1,1,1,1,1] generating graphics... => 10
[6,6] generating graphics... => 20
[6,5,1] generating graphics... => 5
[6,4,2] generating graphics... => 45
[6,4,1,1] generating graphics... => 40
[6,3,3] generating graphics... => 30
[6,3,2,1] generating graphics... => 0
[6,3,1,1,1] generating graphics... => 16
[6,2,2,2] generating graphics... => 45
[6,2,2,1,1] generating graphics... => 36
[6,2,1,1,1,1] generating graphics... => 20
[6,1,1,1,1,1,1] generating graphics... => 10
[5,5,2] generating graphics... => 40
[5,5,1,1] generating graphics... => 45
[5,4,3] generating graphics... => 0
[5,4,2,1] generating graphics... => 5
[5,4,1,1,1] generating graphics... => 0
[5,3,3,1] generating graphics... => 30
[5,3,2,2] generating graphics... => 45
[5,3,2,1,1] generating graphics... => 20
[5,3,1,1,1,1] generating graphics... => 36
[5,2,2,2,1] generating graphics... => 0
[5,2,2,1,1,1] generating graphics... => 16
[5,2,1,1,1,1,1] generating graphics... => 0
[5,1,1,1,1,1,1,1] generating graphics... => 10
[4,4,4] generating graphics... => 30
[4,4,3,1] generating graphics... => 30
[4,4,2,2] generating graphics... => 80
[4,4,2,1,1] generating graphics... => 45
[4,4,1,1,1,1] generating graphics... => 45
[4,3,3,2] generating graphics... => 30
[4,3,3,1,1] generating graphics... => 30
[4,3,2,2,1] generating graphics... => 5
[4,3,2,1,1,1] generating graphics... => 0
[4,3,1,1,1,1,1] generating graphics... => 9
[4,2,2,2,2] generating graphics... => 45
[4,2,2,2,1,1] generating graphics... => 40
[4,2,2,1,1,1,1] generating graphics... => 24
[4,2,1,1,1,1,1,1] generating graphics... => 15
[4,1,1,1,1,1,1,1,1] generating graphics... => 5
[3,3,3,3] generating graphics... => 30
[3,3,3,2,1] generating graphics... => 0
[3,3,3,1,1,1] generating graphics... => 30
[3,3,2,2,2] generating graphics... => 40
[3,3,2,2,1,1] generating graphics... => 45
[3,3,2,1,1,1,1] generating graphics... => 15
[3,3,1,1,1,1,1,1] generating graphics... => 24
[3,2,2,2,2,1] generating graphics... => 5
[3,2,2,2,1,1,1] generating graphics... => 0
[3,2,2,1,1,1,1,1] generating graphics... => 9
[3,2,1,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 5
[2,2,2,2,2,2] generating graphics... => 20
[2,2,2,2,2,1,1] generating graphics... => 15
[2,2,2,2,1,1,1,1] generating graphics... => 15
[2,2,2,1,1,1,1,1,1] generating graphics... => 6
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 6
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The number of self-evacuating tableaux of given shape.
This is the same as the number of standard domino tableaux of the given shape.
References
[1] Stembridge, J. R. Canonical bases and self-evacuating tableaux MathSciNet:1387685
Code
def statistic_alt(la):
    chi = SymmetricGroupRepresentation(la)
    r = abs(ZZ(chi.to_character()(Permutation(range(la.size(),0,-1)))))
    assert r==statistic(la)
    return r

def statistic(la):
    n = la.size()
    la = la + [0]*(n-len(la))

    E_la = sorted([la[j] + n-j-1 for j in range(n) if is_even(la[j] + n-j-1)], reverse=True)
    rE = len(E_la)
    la_e = [ZZ(E_la[i]/2-rE+i+1) for i in range(rE)]
    
    O_la = sorted([la[j] + n-j-2 for j in range(n) if is_even(la[j] +n-j-2)], reverse=True)
    rO = len(O_la)
    la_o = [ZZ(O_la[i]/2-rO+i+1) for i in range(rO)]

    if abs(rE - rO)<=1:
        return (binomial(n//2, sum(la_e))*
                StandardTableaux(la_e).cardinality()*
                StandardTableaux(la_o).cardinality())
    else:
        return 0

Created
Sep 26, 2016 at 23:00 by Martin Rubey
Updated
Sep 26, 2016 at 23:00 by Martin Rubey