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Matching statistic: St001930
Mapping
St001930: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 1
01 => 0
10 => 1
11 => 1
000 => 3
001 => 1
010 => 2
011 => 2
100 => 3
101 => 1
110 => 3
111 => 3
0000 => 6
0001 => 3
0010 => 4
0011 => 4
0100 => 5
0101 => 2
0110 => 5
0111 => 5
1000 => 6
1001 => 3
1010 => 4
1011 => 4
1100 => 6
1101 => 3
1110 => 6
1111 => 6
00000 => 10
00001 => 6
00010 => 7
00011 => 7
00100 => 8
00101 => 4
00110 => 8
00111 => 8
01000 => 9
01001 => 5
01010 => 6
01011 => 6
01100 => 9
01101 => 5
01110 => 9
01111 => 9
10000 => 10
10001 => 6
10010 => 7
10011 => 7
Description
The weak major index of a binary word. This is the sum of the positions of the weak descents, that is, for a word $w = (w_1,\dots,w_n)$, $$ \sum_{\substack{1\leq i < n\\ w_i\geq w_{i+1}}} i. $$