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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000288
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
Description: The number of ones in a binary word.
This is also known as the Hamming weight of the word.
-----------------------------------------------------------------------------
References: [1] [[wikipedia:Hamming_weight]]
-----------------------------------------------------------------------------
Code:
def statistic(x):
return x.count(1)
-----------------------------------------------------------------------------
Statistic values:
0 => 0
1 => 1
00 => 0
01 => 1
10 => 1
11 => 2
000 => 0
001 => 1
010 => 1
011 => 2
100 => 1
101 => 2
110 => 2
111 => 3
0000 => 0
0001 => 1
0010 => 1
0011 => 2
0100 => 1
0101 => 2
0110 => 2
0111 => 3
1000 => 1
1001 => 2
1010 => 2
1011 => 3
1100 => 2
1101 => 3
1110 => 3
1111 => 4
00000 => 0
00001 => 1
00010 => 1
00011 => 2
00100 => 1
00101 => 2
00110 => 2
00111 => 3
01000 => 1
01001 => 2
01010 => 2
01011 => 3
01100 => 2
01101 => 3
01110 => 3
01111 => 4
10000 => 1
10001 => 2
10010 => 2
10011 => 3
10100 => 2
10101 => 3
10110 => 3
10111 => 4
11000 => 2
11001 => 3
11010 => 3
11011 => 4
11100 => 3
11101 => 4
11110 => 4
11111 => 5
000000 => 0
000001 => 1
000010 => 1
000011 => 2
000100 => 1
000101 => 2
000110 => 2
000111 => 3
001000 => 1
001001 => 2
001010 => 2
001011 => 3
001100 => 2
001101 => 3
001110 => 3
001111 => 4
010000 => 1
010001 => 2
010010 => 2
010011 => 3
010100 => 2
010101 => 3
010110 => 3
010111 => 4
011000 => 2
011001 => 3
011010 => 3
011011 => 4
011100 => 3
011101 => 4
011110 => 4
011111 => 5
100000 => 1
100001 => 2
100010 => 2
100011 => 3
100100 => 2
100101 => 3
100110 => 3
100111 => 4
101000 => 2
101001 => 3
101010 => 3
101011 => 4
101100 => 3
101101 => 4
101110 => 4
101111 => 5
110000 => 2
110001 => 3
110010 => 3
110011 => 4
110100 => 3
110101 => 4
110110 => 4
110111 => 5
111000 => 3
111001 => 4
111010 => 4
111011 => 5
111100 => 4
111101 => 5
111110 => 5
111111 => 6
0000000 => 0
0000001 => 1
0000010 => 1
0000011 => 2
0000100 => 1
0000101 => 2
0000110 => 2
0000111 => 3
0001000 => 1
0001001 => 2
0001010 => 2
0001011 => 3
0001100 => 2
0001101 => 3
0001110 => 3
0001111 => 4
0010000 => 1
0010001 => 2
0010010 => 2
0010011 => 3
0010100 => 2
0010101 => 3
0010110 => 3
0010111 => 4
0011000 => 2
0011001 => 3
0011010 => 3
0011011 => 4
0011100 => 3
0011101 => 4
0011110 => 4
0011111 => 5
0100000 => 1
0100001 => 2
0100010 => 2
0100011 => 3
0100100 => 2
0100101 => 3
0100110 => 3
0100111 => 4
0101000 => 2
0101001 => 3
0101010 => 3
0101011 => 4
0101100 => 3
0101101 => 4
0101110 => 4
0101111 => 5
0110000 => 2
0110001 => 3
0110010 => 3
0110011 => 4
0110100 => 3
0110101 => 4
0110110 => 4
0110111 => 5
0111000 => 3
0111001 => 4
0111010 => 4
0111011 => 5
0111100 => 4
0111101 => 5
0111110 => 5
0111111 => 6
1000000 => 1
1000001 => 2
1000010 => 2
1000011 => 3
1000100 => 2
1000101 => 3
1000110 => 3
1000111 => 4
1001000 => 2
1001001 => 3
1001010 => 3
1001011 => 4
1001100 => 3
1001101 => 4
1001110 => 4
1001111 => 5
1010000 => 2
1010001 => 3
1010010 => 3
1010011 => 4
1010100 => 3
1010101 => 4
1010110 => 4
1010111 => 5
1011000 => 3
1011001 => 4
1011010 => 4
1011011 => 5
1011100 => 4
1011101 => 5
1011110 => 5
1011111 => 6
1100000 => 2
1100001 => 3
1100010 => 3
1100011 => 4
1100100 => 3
1100101 => 4
1100110 => 4
1100111 => 5
1101000 => 3
1101001 => 4
1101010 => 4
1101011 => 5
1101100 => 4
1101101 => 5
1101110 => 5
1101111 => 6
1110000 => 3
1110001 => 4
1110010 => 4
1110011 => 5
1110100 => 4
1110101 => 5
1110110 => 5
1110111 => 6
1111000 => 4
1111001 => 5
1111010 => 5
1111011 => 6
1111100 => 5
1111101 => 6
1111110 => 6
1111111 => 7
00000000 => 0
00000001 => 1
00000010 => 1
00000011 => 2
00000100 => 1
00000101 => 2
00000110 => 2
00000111 => 3
00001000 => 1
00001001 => 2
00001010 => 2
00001011 => 3
00001100 => 2
00001101 => 3
00001110 => 3
00001111 => 4
00010000 => 1
00010001 => 2
00010010 => 2
00010011 => 3
00010100 => 2
00010101 => 3
00010110 => 3
00010111 => 4
00011000 => 2
00011001 => 3
00011010 => 3
00011011 => 4
00011100 => 3
00011101 => 4
00011110 => 4
00011111 => 5
00100000 => 1
00100001 => 2
00100010 => 2
00100011 => 3
00100100 => 2
00100101 => 3
00100110 => 3
00100111 => 4
00101000 => 2
00101001 => 3
00101010 => 3
00101011 => 4
00101100 => 3
00101101 => 4
00101110 => 4
00101111 => 5
00110000 => 2
00110001 => 3
00110010 => 3
00110011 => 4
00110100 => 3
00110101 => 4
00110110 => 4
00110111 => 5
00111000 => 3
00111001 => 4
00111010 => 4
00111011 => 5
00111100 => 4
00111101 => 5
00111110 => 5
00111111 => 6
01000000 => 1
01000001 => 2
01000010 => 2
01000011 => 3
01000100 => 2
01000101 => 3
01000110 => 3
01000111 => 4
01001000 => 2
01001001 => 3
01001010 => 3
01001011 => 4
01001100 => 3
01001101 => 4
01001110 => 4
01001111 => 5
01010000 => 2
01010001 => 3
01010010 => 3
01010011 => 4
01010100 => 3
01010101 => 4
01010110 => 4
01010111 => 5
01011000 => 3
01011001 => 4
01011010 => 4
01011011 => 5
01011100 => 4
01011101 => 5
01011110 => 5
01011111 => 6
01100000 => 2
01100001 => 3
01100010 => 3
01100011 => 4
01100100 => 3
01100101 => 4
01100110 => 4
01100111 => 5
01101000 => 3
01101001 => 4
01101010 => 4
01101011 => 5
01101100 => 4
01101101 => 5
01101110 => 5
01101111 => 6
01110000 => 3
01110001 => 4
01110010 => 4
01110011 => 5
01110100 => 4
01110101 => 5
01110110 => 5
01110111 => 6
01111000 => 4
01111001 => 5
01111010 => 5
01111011 => 6
01111100 => 5
01111101 => 6
01111110 => 6
01111111 => 7
10000000 => 1
10000001 => 2
10000010 => 2
10000011 => 3
10000100 => 2
10000101 => 3
10000110 => 3
10000111 => 4
10001000 => 2
10001001 => 3
10001010 => 3
10001011 => 4
10001100 => 3
10001101 => 4
10001110 => 4
10001111 => 5
10010000 => 2
10010001 => 3
10010010 => 3
10010011 => 4
10010100 => 3
10010101 => 4
10010110 => 4
10010111 => 5
10011000 => 3
10011001 => 4
10011010 => 4
10011011 => 5
10011100 => 4
10011101 => 5
10011110 => 5
10011111 => 6
10100000 => 2
10100001 => 3
10100010 => 3
10100011 => 4
10100100 => 3
10100101 => 4
10100110 => 4
10100111 => 5
10101000 => 3
10101001 => 4
10101010 => 4
10101011 => 5
10101100 => 4
10101101 => 5
10101110 => 5
10101111 => 6
10110000 => 3
10110001 => 4
10110010 => 4
10110011 => 5
10110100 => 4
10110101 => 5
10110110 => 5
10110111 => 6
10111000 => 4
10111001 => 5
10111010 => 5
10111011 => 6
10111100 => 5
10111101 => 6
10111110 => 6
10111111 => 7
11000000 => 2
11000001 => 3
11000010 => 3
11000011 => 4
11000100 => 3
11000101 => 4
11000110 => 4
11000111 => 5
11001000 => 3
11001001 => 4
11001010 => 4
11001011 => 5
11001100 => 4
11001101 => 5
11001110 => 5
11001111 => 6
11010000 => 3
11010001 => 4
11010010 => 4
11010011 => 5
11010100 => 4
11010101 => 5
11010110 => 5
11010111 => 6
11011000 => 4
11011001 => 5
11011010 => 5
11011011 => 6
11011100 => 5
11011101 => 6
11011110 => 6
11011111 => 7
11100000 => 3
11100001 => 4
11100010 => 4
11100011 => 5
11100100 => 4
11100101 => 5
11100110 => 5
11100111 => 6
11101000 => 4
11101001 => 5
11101010 => 5
11101011 => 6
11101100 => 5
11101101 => 6
11101110 => 6
11101111 => 7
11110000 => 4
11110001 => 5
11110010 => 5
11110011 => 6
11110100 => 5
11110101 => 6
11110110 => 6
11110111 => 7
11111000 => 5
11111001 => 6
11111010 => 6
11111011 => 7
11111100 => 6
11111101 => 7
11111110 => 7
11111111 => 8
000000000 => 0
000000001 => 1
000000010 => 1
000000011 => 2
000000100 => 1
000000101 => 2
000000111 => 3
000001000 => 1
000001001 => 2
000001010 => 2
000001011 => 3
000001101 => 3
000001111 => 4
000010000 => 1
000010001 => 2
000010010 => 2
000010011 => 3
000010101 => 3
000010111 => 4
000011001 => 3
000011101 => 4
000011111 => 5
000100000 => 1
000100001 => 2
000100010 => 2
000100011 => 3
000100100 => 2
000100101 => 3
000100111 => 4
000101000 => 2
000101010 => 3
000101011 => 4
000101101 => 4
000101111 => 5
000110101 => 4
000111101 => 5
000111111 => 6
001000000 => 1
001000001 => 2
001000010 => 2
001000100 => 2
001000101 => 3
001001000 => 2
001001001 => 3
001001010 => 3
001001011 => 4
001001101 => 4
001001111 => 5
001010001 => 3
001010010 => 3
001010100 => 3
001010101 => 4
001010111 => 5
001011101 => 5
001011111 => 6
001100001 => 3
001101101 => 5
001111101 => 6
001111111 => 7
010000000 => 1
010000001 => 2
010000010 => 2
010000011 => 3
010000100 => 2
010000101 => 3
010000110 => 3
010000111 => 4
010001000 => 2
010001001 => 3
010001010 => 3
010001011 => 4
010001101 => 4
010001111 => 5
010010000 => 2
010010001 => 3
010010010 => 3
010010011 => 4
010010100 => 3
010010101 => 4
010010111 => 5
010011011 => 5
010011101 => 5
010011111 => 6
010100000 => 2
010100001 => 3
010100010 => 3
010100100 => 3
010100101 => 4
010100111 => 5
010101000 => 3
010101001 => 4
010101010 => 4
010101011 => 5
010101111 => 6
010110001 => 4
010110111 => 6
010111101 => 6
010111111 => 7
011000001 => 3
011001001 => 4
011001111 => 6
011010001 => 4
011011001 => 5
011011101 => 6
011011111 => 7
011100001 => 4
011100101 => 5
011101001 => 5
011101101 => 6
011101111 => 7
011110001 => 5
011110011 => 6
011110101 => 6
011110111 => 7
011111001 => 6
011111011 => 7
011111101 => 7
011111111 => 8
100000000 => 1
100000010 => 2
100000100 => 2
100000110 => 3
100001000 => 2
100001010 => 3
100001100 => 3
100001110 => 4
100010000 => 2
100010001 => 3
100010010 => 3
100010100 => 3
100010110 => 4
100011010 => 4
100011100 => 4
100011110 => 5
100100000 => 2
100100010 => 3
100100100 => 3
100100101 => 4
100100110 => 4
100101001 => 4
100101010 => 4
100101100 => 4
100101110 => 5
100110010 => 4
100110100 => 4
100110110 => 5
100111010 => 5
100111101 => 6
100111110 => 6
101000000 => 2
101000100 => 3
101000110 => 4
101001000 => 3
101001001 => 4
101001010 => 4
101001100 => 4
101001110 => 5
101010000 => 3
101010010 => 4
101010100 => 4
101010101 => 5
101010110 => 5
101011010 => 5
101011110 => 6
101100110 => 5
101101010 => 5
101101110 => 6
101111101 => 7
101111110 => 7
110000000 => 2
110001000 => 3
110001110 => 5
110010000 => 3
110010010 => 4
110010100 => 4
110010110 => 5
110011010 => 5
110011110 => 6
110100000 => 3
110100100 => 4
110100110 => 5
110101000 => 4
110101010 => 5
110110110 => 6
110111101 => 7
110111110 => 7
111000000 => 3
111001000 => 4
111001110 => 6
111010000 => 4
111010100 => 5
111010110 => 6
111011110 => 7
111100000 => 4
111100100 => 5
111101000 => 5
111101010 => 6
111101110 => 7
111110000 => 5
111110100 => 6
111111000 => 6
111111010 => 7
111111100 => 7
111111101 => 8
111111110 => 8
111111111 => 9
1010101010 => 5
1010101100 => 5
1010110010 => 5
1010110100 => 5
1010111000 => 5
1011001010 => 5
1011001100 => 5
1011010010 => 5
1011010100 => 5
1011011000 => 5
1011100010 => 5
1011100100 => 5
1011101000 => 5
1011110000 => 5
1100101010 => 5
1100101100 => 5
1100110010 => 5
1100110100 => 5
1100111000 => 5
1101001010 => 5
1101001100 => 5
1101010010 => 5
1101010100 => 5
1101011000 => 5
1101100010 => 5
1101100100 => 5
1101101000 => 5
1101110000 => 5
1110001010 => 5
1110001100 => 5
1110010010 => 5
1110010100 => 5
1110011000 => 5
1110100010 => 5
1110100100 => 5
1110101000 => 5
1110110000 => 5
1111000010 => 5
1111000100 => 5
1111001000 => 5
1111010000 => 5
1111100000 => 5
1111111110 => 9
1111111101 => 9
1111000001 => 5
1110111110 => 8
1110100001 => 5
1110011110 => 7
1110010001 => 5
1110001001 => 5
1110000101 => 5
1101111110 => 8
1101100001 => 5
1101010001 => 5
1101001110 => 6
1101001001 => 5
1101000101 => 5
1100110001 => 5
1100101001 => 5
1100100110 => 5
1100100101 => 5
1100011001 => 5
1100010101 => 5
1100010010 => 4
1100001000 => 3
1011111110 => 8
1011111101 => 8
1011100001 => 5
1011010001 => 5
1011001001 => 5
1011000101 => 5
1010111110 => 7
1010110001 => 5
1010101001 => 5
1010100110 => 5
1010100101 => 5
1010011010 => 5
1010011001 => 5
1010010110 => 5
1010010101 => 5
1010001110 => 5
1001111110 => 7
1001111000 => 5
1001110100 => 5
1001110001 => 5
1001101100 => 5
1001101010 => 5
1001101001 => 5
1001100110 => 5
1001100101 => 5
1001011110 => 6
1001011010 => 5
1001011001 => 5
1001010110 => 5
1001010101 => 5
1001001110 => 5
1000111110 => 6
1000111100 => 5
1000111010 => 5
1000110110 => 5
1000101110 => 5
1000011110 => 5
1000010110 => 4
1000001110 => 4
1000001010 => 3
1000000110 => 3
1000000100 => 2
1000000010 => 2
1000000000 => 1
0111111111 => 9
0111111101 => 8
0111111001 => 7
0111110001 => 6
0111100001 => 5
0111000001 => 4
0110000001 => 3
0100000001 => 2
0000000001 => 1
0111111011 => 8
0111110101 => 7
0111101001 => 6
0111010001 => 5
0110100001 => 4
0101000001 => 3
0010000001 => 2
0101010101 => 5
0101010011 => 5
0101001101 => 5
0101001011 => 5
0101000111 => 5
0100110101 => 5
0100110011 => 5
0100101101 => 5
0100101011 => 5
0100100111 => 5
0100011101 => 5
0100011011 => 5
0100010111 => 5
0100001111 => 5
0011010101 => 5
0011010011 => 5
0011001101 => 5
0011001011 => 5
0011000111 => 5
0010110101 => 5
0010110011 => 5
0010101101 => 5
0010101011 => 5
0010100111 => 5
0010011101 => 5
0010011011 => 5
0010010111 => 5
0010001111 => 5
0001110101 => 5
0001110011 => 5
0001101101 => 5
0001101011 => 5
0001100111 => 5
0001011101 => 5
0001011011 => 5
0001010111 => 5
0001001111 => 5
0000111101 => 5
0000111011 => 5
0000110111 => 5
0000101111 => 5
0000011111 => 5
0100000010 => 2
0010111100 => 5
0011110100 => 5
0111010100 => 5
0000000010 => 1
0000111110 => 5
0100000000 => 1
0100000011 => 3
0100000111 => 4
0100011111 => 6
0100111111 => 7
0101111111 => 8
0100000101 => 3
0100001011 => 4
0100101111 => 6
0101011111 => 7
0110111111 => 8
0101010110 => 5
0101011001 => 5
0101011010 => 5
0101011100 => 5
0101100101 => 5
0101100110 => 5
0101101001 => 5
0101101010 => 5
0101101100 => 5
0101110001 => 5
0101110010 => 5
0101110100 => 5
0101111000 => 5
0110010101 => 5
0110010110 => 5
0110011001 => 5
0110011010 => 5
0110011100 => 5
0110100101 => 5
0110100110 => 5
0110101001 => 5
0110101010 => 5
0110101100 => 5
0110110001 => 5
0110110010 => 5
0110110100 => 5
0110111000 => 5
0111000101 => 5
0111000110 => 5
0111001001 => 5
0111001010 => 5
0111001100 => 5
0111010010 => 5
0111011000 => 5
0111100010 => 5
0111100100 => 5
0111101000 => 5
0111110000 => 5
0100000100 => 2
0011100110 => 5
0011101010 => 5
0011101100 => 5
0001101110 => 5
0010110110 => 5
0011110010 => 5
0001110110 => 5
0100111010 => 5
0010111010 => 5
0011111000 => 5
0001111010 => 5
0100111100 => 5
0001111100 => 5
0000000101 => 2
0000001101 => 3
0000011101 => 4
0001111101 => 6
0011111101 => 7
0000001001 => 2
0000010101 => 3
0000101101 => 4
0010111101 => 6
0101111101 => 7
10000000000 => 1
10000000010 => 2
10000000110 => 3
10000001110 => 4
10000011110 => 5
10000111110 => 6
10001111110 => 7
10011111110 => 8
10111111110 => 9
11111111110 => 10
10000000100 => 2
10000001010 => 3
10000010110 => 4
10000101110 => 5
10001011110 => 6
10010111110 => 7
10101111110 => 8
11011111110 => 9
10000010000 => 2
10000100010 => 3
10001000010 => 3
10000100100 => 3
10001001010 => 4
10001000100 => 3
10000101000 => 3
10010001010 => 4
10001010010 => 4
10010000100 => 3
10001001000 => 3
10010010010 => 4
10001010100 => 4
10010101010 => 5
10010001000 => 3
10100010010 => 4
10010100010 => 4
10010010100 => 4
10100101010 => 5
01111111111 => 10
01111111101 => 9
01111111001 => 8
01111110001 => 7
01111100001 => 6
01111000001 => 5
01110000001 => 4
01100000001 => 3
01000000001 => 2
00000000001 => 1
00000000010 => 1
10101010101 => 6
10101010010 => 5
10101001001 => 5
10101001010 => 5
10101000100 => 4
10100100101 => 5
10100100010 => 4
10100101001 => 5
10100100100 => 4
10100010001 => 4
10100010100 => 4
10100001000 => 3
10010010101 => 5
10010001001 => 4
10010100101 => 5
10010101001 => 5
10010100100 => 4
10010010001 => 4
10001000101 => 4
10001001001 => 4
10001010001 => 4
10000100001 => 3
01001010101 => 5
01001010010 => 4
01001001001 => 4
01001001010 => 4
01001000100 => 3
01000100101 => 4
01000100010 => 3
01000101001 => 4
01000101010 => 4
01000100100 => 3
01000010001 => 3
01000010010 => 3
01000010100 => 3
01000001000 => 2
01010010101 => 5
01010010010 => 4
01010001001 => 4
01010001010 => 4
01010000100 => 3
01010100101 => 5
01010100010 => 4
01010101001 => 5
01010101010 => 5
01010100100 => 4
01010010001 => 4
01010010100 => 4
01010001000 => 3
01001000101 => 4
01001000010 => 3
01001010001 => 4
01001010100 => 4
01001001000 => 3
01000100001 => 3
01000101000 => 3
01000010000 => 2
00100010101 => 4
00100010010 => 3
00100001001 => 3
00100001010 => 3
00100000100 => 2
00100100101 => 4
00100100010 => 3
00100101001 => 4
00100101010 => 4
00100100100 => 3
00100010001 => 3
00100010100 => 3
00100001000 => 2
00101000101 => 4
00101000010 => 3
00101001001 => 4
00101001010 => 4
00101000100 => 3
00101010001 => 4
00101010010 => 4
00101010100 => 4
00101001000 => 3
00100100001 => 3
00100101000 => 3
00100010000 => 2
00010000101 => 3
00010000010 => 2
00010001001 => 3
00010001010 => 3
00010000100 => 2
00010010001 => 3
00010010010 => 3
00010010100 => 3
00010001000 => 2
00010100001 => 3
00010100010 => 3
00010100100 => 3
00010101000 => 3
00010010000 => 2
00001000001 => 2
00001000010 => 2
00001000100 => 2
00001001000 => 2
00001010000 => 2
00000100000 => 1
01000000000 => 1
01000000011 => 3
01000000111 => 4
01000001111 => 5
01000011111 => 6
01000111111 => 7
01001111111 => 8
01011111111 => 9
00000000101 => 2
00000001101 => 3
00000011101 => 4
00000111101 => 5
00001111101 => 6
00011111101 => 7
00111111101 => 8
11111111101 => 10
101010101010 => 6
101010101100 => 6
101010110010 => 6
101010110100 => 6
101010111000 => 6
101011001010 => 6
101011001100 => 6
101011010010 => 6
101011010100 => 6
101011011000 => 6
101011100010 => 6
101011100100 => 6
101011101000 => 6
101011110000 => 6
101100101010 => 6
101100101100 => 6
101100110010 => 6
101100110100 => 6
101100111000 => 6
101101001010 => 6
101101001100 => 6
101101010010 => 6
101101010100 => 6
101101011000 => 6
101101100010 => 6
101101100100 => 6
101101101000 => 6
101101110000 => 6
101110001010 => 6
101110001100 => 6
101110010010 => 6
101110010100 => 6
101110011000 => 6
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-----------------------------------------------------------------------------
Created: Nov 06, 2015 at 16:56 by Martin Rubey
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Last Updated: Dec 02, 2021 at 15:53 by Martin Rubey