Identifier
- St000347: Binary words ⟶ ℤ
Values
0 => 0
1 => 0
00 => 0
01 => 0
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 0
100 => 3
101 => 1
110 => 3
111 => 0
0000 => 0
0001 => 0
0010 => 1
0011 => 0
0100 => 3
0101 => 1
0110 => 3
0111 => 0
1000 => 6
1001 => 3
1010 => 5
1011 => 1
1100 => 8
1101 => 3
1110 => 6
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 3
00101 => 1
00110 => 3
00111 => 0
01000 => 6
01001 => 3
01010 => 5
01011 => 1
01100 => 8
01101 => 3
01110 => 6
01111 => 0
10000 => 10
10001 => 6
10010 => 8
10011 => 3
10100 => 11
10101 => 5
10110 => 8
10111 => 1
11000 => 15
11001 => 8
11010 => 11
11011 => 3
11100 => 15
11101 => 6
11110 => 10
11111 => 0
000000 => 0
000001 => 0
000010 => 1
000011 => 0
000100 => 3
000101 => 1
000110 => 3
000111 => 0
001000 => 6
001001 => 3
001010 => 5
001011 => 1
001100 => 8
001101 => 3
001110 => 6
001111 => 0
010000 => 10
010001 => 6
010010 => 8
010011 => 3
010100 => 11
010101 => 5
010110 => 8
010111 => 1
011000 => 15
011001 => 8
011010 => 11
011011 => 3
011100 => 15
011101 => 6
011110 => 10
011111 => 0
100000 => 15
100001 => 10
100010 => 12
100011 => 6
100100 => 15
100101 => 8
100110 => 11
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Description
The inversion sum of a binary word.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.
References
[1] The inversion sum of a permutation. St000055
Code
def statistic(w):
return sum( inv[1]-inv[0] for inv in w.inversions() )
Created
Dec 26, 2015 at 14:34 by Christian Stump
Updated
Dec 26, 2015 at 14:34 by Christian Stump
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