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Matching statistic: St001355
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Mapping
St001355: 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 => 1
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 1
100 => 1
101 => 1
110 => 0
111 => 0
0000 => 0
0001 => 0
0010 => 0
0011 => 1
0100 => 1
0101 => 2
0110 => 2
0111 => 1
1000 => 1
1001 => 2
1010 => 2
1011 => 1
1100 => 1
1101 => 0
1110 => 0
1111 => 0
00000 => 0
00001 => 0
00010 => 0
00011 => 0
00100 => 0
00101 => 0
00110 => 1
00111 => 1
01000 => 1
01001 => 1
01010 => 2
01011 => 2
01100 => 2
01101 => 2
01110 => 1
01111 => 1
10000 => 1
10001 => 1
10010 => 2
10011 => 2
Description
Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. Graphically, this is the number of returns to the main diagonal of the monotone lattice path of a binary word.