Identifier
- St000348: Binary words ⟶ ℤ
Values
0 => 0
1 => 0
00 => 0
01 => 1
10 => 0
11 => 0
000 => 0
001 => 3
010 => 1
011 => 3
100 => 0
101 => 1
110 => 0
111 => 0
0000 => 0
0001 => 6
0010 => 3
0011 => 8
0100 => 1
0101 => 5
0110 => 3
0111 => 6
1000 => 0
1001 => 3
1010 => 1
1011 => 3
1100 => 0
1101 => 1
1110 => 0
1111 => 0
00000 => 0
00001 => 10
00010 => 6
00011 => 15
00100 => 3
00101 => 11
00110 => 8
00111 => 15
01000 => 1
01001 => 8
01010 => 5
01011 => 11
01100 => 3
01101 => 8
01110 => 6
01111 => 10
10000 => 0
10001 => 6
10010 => 3
10011 => 8
10100 => 1
10101 => 5
10110 => 3
10111 => 6
11000 => 0
11001 => 3
11010 => 1
11011 => 3
11100 => 0
11101 => 1
11110 => 0
11111 => 0
000000 => 0
000001 => 15
000010 => 10
000011 => 24
000100 => 6
000101 => 19
000110 => 15
000111 => 27
001000 => 3
001001 => 15
001010 => 11
001011 => 22
001100 => 8
001101 => 18
001110 => 15
001111 => 24
010000 => 1
010001 => 12
010010 => 8
010011 => 18
010100 => 5
010101 => 14
010110 => 11
010111 => 19
011000 => 3
011001 => 11
011010 => 8
011011 => 15
011100 => 6
011101 => 12
011110 => 10
011111 => 15
100000 => 0
100001 => 10
100010 => 6
100011 => 15
100100 => 3
100101 => 11
100110 => 8
>>> Load all 1200 entries. <<<
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The non-inversion sum of a binary word.
A pair $a < b$ is an noninversion of a binary word $w = w_1 \cdots w_n$ if $w_a < w_b$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $w$.
A pair $a < b$ is an noninversion of a binary word $w = w_1 \cdots w_n$ if $w_a < w_b$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $w$.
References
[1] The non-inversion sum of a permutation. St000341
Code
def statistic(w):
return sum( b-a for a in range(len(w)) for b in range(a,len(w)) if w[a] < w[b] )
Created
Dec 26, 2015 at 14:39 by Christian Stump
Updated
Dec 26, 2015 at 14:39 by Christian Stump
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!