Identifier
- St001930: Binary words ⟶ ℤ
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
10100 => 8
10101 => 4
10110 => 8
10111 => 8
11000 => 10
11001 => 6
11010 => 7
11011 => 7
11100 => 10
11101 => 6
11110 => 10
11111 => 10
000000 => 15
000001 => 10
000010 => 11
000011 => 11
000100 => 12
000101 => 7
000110 => 12
000111 => 12
001000 => 13
001001 => 8
001010 => 9
001011 => 9
001100 => 13
001101 => 8
001110 => 13
001111 => 13
010000 => 14
010001 => 9
010010 => 10
010011 => 10
010100 => 11
010101 => 6
010110 => 11
010111 => 11
011000 => 14
011001 => 9
011010 => 10
011011 => 10
011100 => 14
011101 => 9
011110 => 14
011111 => 14
100000 => 15
100001 => 10
100010 => 11
100011 => 11
100100 => 12
100101 => 7
100110 => 12
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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 $w = (w_1,\dots,w_n)$,
$$ \sum_{\substack{1\leq i < n\\ w_i\geq w_{i+1}}} i. $$
This is the sum of the positions of the weak descents, that is, for a word $w = (w_1,\dots,w_n)$,
$$ \sum_{\substack{1\leq i < n\\ w_i\geq w_{i+1}}} i. $$
Code
def statistic(w):
return sum(i for i in range(1, len(w)) if w[i-1] >= w[i])
Created
Nov 05, 2023 at 15:59 by Martin Rubey
Updated
Nov 05, 2023 at 15:59 by Martin Rubey
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