Identifier
- St001485: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>0
01=>0
10=>1
11=>0
000=>0
001=>0
010=>2
011=>0
100=>1
101=>1
110=>2
111=>0
0000=>0
0001=>0
0010=>3
0011=>0
0100=>2
0101=>2
0110=>3
0111=>0
1000=>1
1001=>1
1010=>0
1011=>1
1100=>2
1101=>2
1110=>3
1111=>0
00000=>0
00001=>0
00010=>4
00011=>0
00100=>3
00101=>3
00110=>4
00111=>0
01000=>2
01001=>2
01010=>1
01011=>2
01100=>3
01101=>3
01110=>4
01111=>0
10000=>1
10001=>1
10010=>0
10011=>1
10100=>4
10101=>4
10110=>0
10111=>1
11000=>2
11001=>2
11010=>1
11011=>2
11100=>3
11101=>3
11110=>4
11111=>0
000000=>0
000001=>0
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000011=>0
000100=>4
000101=>4
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000111=>0
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001011=>3
001100=>4
001101=>4
001110=>5
001111=>0
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010010=>1
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010100=>0
010101=>0
010110=>1
010111=>2
011000=>3
011001=>3
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011011=>3
011100=>4
011101=>4
011110=>5
011111=>0
100000=>1
100001=>1
100010=>0
100011=>1
100100=>5
100101=>5
100110=>0
100111=>1
101000=>4
101001=>4
101010=>3
101011=>4
101100=>5
101101=>5
101110=>0
101111=>1
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110001=>2
110010=>1
110011=>2
110100=>0
110101=>0
110110=>1
110111=>2
111000=>3
111001=>3
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111011=>3
111100=>4
111101=>4
111110=>5
111111=>0
0000000=>0
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0000101=>5
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0101101=>0
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0111110=>6
0111111=>0
1000000=>1
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1001011=>5
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1011001=>5
1011010=>4
1011011=>5
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1011101=>6
1011110=>0
1011111=>1
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1100110=>1
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1101001=>6
1101010=>5
1101011=>6
1101100=>0
1101101=>0
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1110000=>3
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1110111=>3
1111000=>4
1111001=>4
1111010=>3
1111011=>4
1111100=>5
1111101=>5
1111110=>6
1111111=>0
00000000=>0
00000001=>0
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00000011=>0
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00000101=>6
00000110=>7
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00101011=>0
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01111011=>5
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01111101=>6
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10000000=>1
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10001110=>0
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10011110=>0
10011111=>1
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10101011=>1
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10111101=>7
10111110=>0
10111111=>1
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11001001=>7
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11001011=>7
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11010001=>6
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11010011=>6
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11100001=>3
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11100011=>3
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11101101=>1
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11101111=>3
11110000=>4
11110001=>4
11110010=>3
11110011=>4
11110100=>2
11110101=>2
11110110=>3
11110111=>4
11111000=>5
11111001=>5
11111010=>4
11111011=>5
11111100=>6
11111101=>6
11111110=>7
11111111=>0
000000000=>0
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000000010=>8
000000011=>0
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000001001=>6
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001001111=>3
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001010001=>8
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001010011=>8
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001010101=>6
001010110=>7
001010111=>8
001011000=>0
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001011010=>8
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001011100=>1
001011101=>1
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001111001=>6
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010011100=>0
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011110111=>5
011111000=>6
011111001=>6
011111010=>5
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011111100=>7
011111101=>7
011111110=>8
011111111=>0
100000000=>1
100000001=>1
100000010=>0
100000011=>1
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100000110=>0
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100001001=>7
100001010=>6
100001011=>7
100001100=>8
100001101=>8
100001110=>0
100001111=>1
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100010001=>6
100010010=>5
100010011=>6
100010100=>4
100010101=>4
100010110=>5
100010111=>6
100011000=>7
100011001=>7
100011010=>6
100011011=>7
100011100=>8
100011101=>8
100011110=>0
100011111=>1
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100100001=>5
100100010=>4
100100011=>5
100100100=>3
100100101=>3
100100110=>4
100100111=>5
100101000=>2
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100101010=>1
100101011=>2
100101100=>3
100101101=>3
100101110=>4
100101111=>5
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100110011=>6
100110100=>4
100110101=>4
100110110=>5
100110111=>6
100111000=>7
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100111011=>7
100111100=>8
100111101=>8
100111110=>0
100111111=>1
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101000001=>4
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101000011=>4
101000100=>2
101000101=>2
101000110=>3
101000111=>4
101001000=>1
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110001000=>8
110001001=>8
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110010001=>7
110010010=>6
110010011=>7
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110011000=>8
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110011011=>8
110011100=>0
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110011110=>1
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110100000=>6
110100001=>6
110100010=>5
110100011=>6
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110100101=>4
110100110=>5
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110101011=>3
110101100=>4
110101101=>4
110101110=>5
110101111=>6
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110110001=>7
110110010=>6
110110011=>7
110110100=>5
110110101=>5
110110110=>6
110110111=>7
110111000=>8
110111001=>8
110111010=>7
110111011=>8
110111100=>0
110111101=>0
110111110=>1
110111111=>2
111000000=>3
111000001=>3
111000010=>2
111000011=>3
111000100=>1
111000101=>1
111000110=>2
111000111=>3
111001000=>0
111001001=>0
111001010=>8
111001011=>0
111001100=>1
111001101=>1
111001110=>2
111001111=>3
111010000=>8
111010001=>8
111010010=>7
111010011=>8
111010100=>6
111010101=>6
111010110=>7
111010111=>8
111011000=>0
111011001=>0
111011010=>8
111011011=>0
111011100=>1
111011101=>1
111011110=>2
111011111=>3
111100000=>4
111100001=>4
111100010=>3
111100011=>4
111100100=>2
111100101=>2
111100110=>3
111100111=>4
111101000=>1
111101001=>1
111101010=>0
111101011=>1
111101100=>2
111101101=>2
111101110=>3
111101111=>4
111110000=>5
111110001=>5
111110010=>4
111110011=>5
111110100=>3
111110101=>3
111110110=>4
111110111=>5
111111000=>6
111111001=>6
111111010=>5
111111011=>6
111111100=>7
111111101=>7
111111110=>8
111111111=>0
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Description
The modular major index of a binary word.
This is St000290The major index of a binary word. modulo the length of the word.
This is St000290The major index of a binary word. modulo the length of the word.
References
[1] Swanson, J. P. Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics MathSciNet:3885578
Code
def statistic(w): return w.major_index() % len(w)
Created
Oct 24, 2019 at 13:25 by Martin Rubey
Updated
Oct 24, 2019 at 13:25 by Martin Rubey
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