Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001730
(load all 2 compositions to match this statistic)
Mapping
St001730: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 0
01 => 0
10 => 0
11 => 0
000 => 0
001 => 0
010 => 0
011 => 1
100 => 1
101 => 0
110 => 0
111 => 0
0000 => 0
0001 => 0
0010 => 0
0011 => 0
0100 => 0
0101 => 0
0110 => 1
0111 => 1
1000 => 1
1001 => 1
1010 => 0
1011 => 0
1100 => 0
1101 => 0
1110 => 0
1111 => 0
00000 => 0
00001 => 0
00010 => 0
00011 => 0
00100 => 0
00101 => 0
00110 => 0
00111 => 1
01000 => 0
01001 => 0
01010 => 0
01011 => 1
01100 => 2
01101 => 1
01110 => 1
01111 => 1
10000 => 1
10001 => 1
10010 => 1
10011 => 2
Description
The number of times the path corresponding to a binary word crosses the base line. Interpret each $0$ as a step $(1,-1)$ and $1$ as a step $(1,1)$. Then this statistic counts the number of times the path crosses the $x$-axis.