Identifier
- St001524: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>1
01=>0
10=>0
11=>1
000=>1
001=>0
010=>1
011=>0
100=>0
101=>1
110=>0
111=>1
0000=>2
0001=>1
0010=>1
0011=>0
0100=>1
0101=>0
0110=>2
0111=>1
1000=>1
1001=>2
1010=>0
1011=>1
1100=>0
1101=>1
1110=>1
1111=>2
00000=>2
00001=>1
00010=>1
00011=>0
00100=>2
00101=>1
00110=>1
00111=>0
01000=>1
01001=>0
01010=>2
01011=>1
01100=>1
01101=>0
01110=>2
01111=>1
10000=>1
10001=>2
10010=>0
10011=>1
10100=>1
10101=>2
10110=>0
10111=>1
11000=>0
11001=>1
11010=>1
11011=>2
11100=>0
11101=>1
11110=>1
11111=>2
000000=>3
000001=>2
000010=>2
000011=>1
000100=>2
000101=>1
000110=>1
000111=>0
001000=>2
001001=>1
001010=>1
001011=>0
001100=>3
001101=>2
001110=>2
001111=>1
010000=>2
010001=>1
010010=>3
010011=>2
010100=>1
010101=>0
010110=>2
010111=>1
011000=>1
011001=>0
011010=>2
011011=>1
011100=>2
011101=>1
011110=>3
011111=>2
100000=>2
100001=>3
100010=>1
100011=>2
100100=>1
100101=>2
100110=>0
100111=>1
101000=>1
101001=>2
101010=>0
101011=>1
101100=>2
101101=>3
101110=>1
101111=>2
110000=>1
110001=>2
110010=>2
110011=>3
110100=>0
110101=>1
110110=>1
110111=>2
111000=>0
111001=>1
111010=>1
111011=>2
111100=>1
111101=>2
111110=>2
111111=>3
0000000=>3
0000001=>2
0000010=>2
0000011=>1
0000100=>2
0000101=>1
0000110=>1
0000111=>0
0001000=>3
0001001=>2
0001010=>2
0001011=>1
0001100=>2
0001101=>1
0001110=>1
0001111=>0
0010000=>2
0010001=>1
0010010=>1
0010011=>0
0010100=>3
0010101=>2
0010110=>2
0010111=>1
0011000=>2
0011001=>1
0011010=>1
0011011=>0
0011100=>3
0011101=>2
0011110=>2
0011111=>1
0100000=>2
0100001=>1
0100010=>3
0100011=>2
0100100=>1
0100101=>0
0100110=>2
0100111=>1
0101000=>2
0101001=>1
0101010=>3
0101011=>2
0101100=>1
0101101=>0
0101110=>2
0101111=>1
0110000=>1
0110001=>0
0110010=>2
0110011=>1
0110100=>2
0110101=>1
0110110=>3
0110111=>2
0111000=>1
0111001=>0
0111010=>2
0111011=>1
0111100=>2
0111101=>1
0111110=>3
0111111=>2
1000000=>2
1000001=>3
1000010=>1
1000011=>2
1000100=>1
1000101=>2
1000110=>0
1000111=>1
1001000=>2
1001001=>3
1001010=>1
1001011=>2
1001100=>1
1001101=>2
1001110=>0
1001111=>1
1010000=>1
1010001=>2
1010010=>0
1010011=>1
1010100=>2
1010101=>3
1010110=>1
1010111=>2
1011000=>1
1011001=>2
1011010=>0
1011011=>1
1011100=>2
1011101=>3
1011110=>1
1011111=>2
1100000=>1
1100001=>2
1100010=>2
1100011=>3
1100100=>0
1100101=>1
1100110=>1
1100111=>2
1101000=>1
1101001=>2
1101010=>2
1101011=>3
1101100=>0
1101101=>1
1101110=>1
1101111=>2
1110000=>0
1110001=>1
1110010=>1
1110011=>2
1110100=>1
1110101=>2
1110110=>2
1110111=>3
1111000=>0
1111001=>1
1111010=>1
1111011=>2
1111100=>1
1111101=>2
1111110=>2
1111111=>3
00000000=>4
00000001=>3
00000010=>3
00000011=>2
00000100=>3
00000101=>2
00000110=>2
00000111=>1
00001000=>3
00001001=>2
00001010=>2
00001011=>1
00001100=>2
00001101=>1
00001110=>1
00001111=>0
00010000=>3
00010001=>2
00010010=>2
00010011=>1
00010100=>2
00010101=>1
00010110=>1
00010111=>0
00011000=>4
00011001=>3
00011010=>3
00011011=>2
00011100=>3
00011101=>2
00011110=>2
00011111=>1
00100000=>3
00100001=>2
00100010=>2
00100011=>1
00100100=>4
00100101=>3
00100110=>3
00100111=>2
00101000=>2
00101001=>1
00101010=>1
00101011=>0
00101100=>3
00101101=>2
00101110=>2
00101111=>1
00110000=>2
00110001=>1
00110010=>1
00110011=>0
00110100=>3
00110101=>2
00110110=>2
00110111=>1
00111000=>3
00111001=>2
00111010=>2
00111011=>1
00111100=>4
00111101=>3
00111110=>3
00111111=>2
01000000=>3
01000001=>2
01000010=>4
01000011=>3
01000100=>2
01000101=>1
01000110=>3
01000111=>2
01001000=>2
01001001=>1
01001010=>3
01001011=>2
01001100=>1
01001101=>0
01001110=>2
01001111=>1
01010000=>2
01010001=>1
01010010=>3
01010011=>2
01010100=>1
01010101=>0
01010110=>2
01010111=>1
01011000=>3
01011001=>2
01011010=>4
01011011=>3
01011100=>2
01011101=>1
01011110=>3
01011111=>2
01100000=>2
01100001=>1
01100010=>3
01100011=>2
01100100=>3
01100101=>2
01100110=>4
01100111=>3
01101000=>1
01101001=>0
01101010=>2
01101011=>1
01101100=>2
01101101=>1
01101110=>3
01101111=>2
01110000=>1
01110001=>0
01110010=>2
01110011=>1
01110100=>2
01110101=>1
01110110=>3
01110111=>2
01111000=>2
01111001=>1
01111010=>3
01111011=>2
01111100=>3
01111101=>2
01111110=>4
01111111=>3
10000000=>3
10000001=>4
10000010=>2
10000011=>3
10000100=>2
10000101=>3
10000110=>1
10000111=>2
10001000=>2
10001001=>3
10001010=>1
10001011=>2
10001100=>1
10001101=>2
10001110=>0
10001111=>1
10010000=>2
10010001=>3
10010010=>1
10010011=>2
10010100=>1
10010101=>2
10010110=>0
10010111=>1
10011000=>3
10011001=>4
10011010=>2
10011011=>3
10011100=>2
10011101=>3
10011110=>1
10011111=>2
10100000=>2
10100001=>3
10100010=>1
10100011=>2
10100100=>3
10100101=>4
10100110=>2
10100111=>3
10101000=>1
10101001=>2
10101010=>0
10101011=>1
10101100=>2
10101101=>3
10101110=>1
10101111=>2
10110000=>1
10110001=>2
10110010=>0
10110011=>1
10110100=>2
10110101=>3
10110110=>1
10110111=>2
10111000=>2
10111001=>3
10111010=>1
10111011=>2
10111100=>3
10111101=>4
10111110=>2
10111111=>3
11000000=>2
11000001=>3
11000010=>3
11000011=>4
11000100=>1
11000101=>2
11000110=>2
11000111=>3
11001000=>1
11001001=>2
11001010=>2
11001011=>3
11001100=>0
11001101=>1
11001110=>1
11001111=>2
11010000=>1
11010001=>2
11010010=>2
11010011=>3
11010100=>0
11010101=>1
11010110=>1
11010111=>2
11011000=>2
11011001=>3
11011010=>3
11011011=>4
11011100=>1
11011101=>2
11011110=>2
11011111=>3
11100000=>1
11100001=>2
11100010=>2
11100011=>3
11100100=>2
11100101=>3
11100110=>3
11100111=>4
11101000=>0
11101001=>1
11101010=>1
11101011=>2
11101100=>1
11101101=>2
11101110=>2
11101111=>3
11110000=>0
11110001=>1
11110010=>1
11110011=>2
11110100=>1
11110101=>2
11110110=>2
11110111=>3
11111000=>1
11111001=>2
11111010=>2
11111011=>3
11111100=>2
11111101=>3
11111110=>3
11111111=>4
000000000=>4
000000001=>3
000000010=>3
000000011=>2
000000100=>3
000000101=>2
000000110=>2
000000111=>1
000001000=>3
000001001=>2
000001010=>2
000001011=>1
000001100=>2
000001101=>1
000001110=>1
000001111=>0
000010000=>4
000010001=>3
000010010=>3
000010011=>2
000010100=>3
000010101=>2
000010110=>2
000010111=>1
000011000=>3
000011001=>2
000011010=>2
000011011=>1
000011100=>2
000011101=>1
000011110=>1
000011111=>0
000100000=>3
000100001=>2
000100010=>2
000100011=>1
000100100=>2
000100101=>1
000100110=>1
000100111=>0
000101000=>4
000101001=>3
000101010=>3
000101011=>2
000101100=>3
000101101=>2
000101110=>2
000101111=>1
000110000=>3
000110001=>2
000110010=>2
000110011=>1
000110100=>2
000110101=>1
000110110=>1
000110111=>0
000111000=>4
000111001=>3
000111010=>3
000111011=>2
000111100=>3
000111101=>2
000111110=>2
000111111=>1
001000000=>3
001000001=>2
001000010=>2
001000011=>1
001000100=>4
001000101=>3
001000110=>3
001000111=>2
001001000=>2
001001001=>1
001001010=>1
001001011=>0
001001100=>3
001001101=>2
001001110=>2
001001111=>1
001010000=>3
001010001=>2
001010010=>2
001010011=>1
001010100=>4
001010101=>3
001010110=>3
001010111=>2
001011000=>2
001011001=>1
001011010=>1
001011011=>0
001011100=>3
001011101=>2
001011110=>2
001011111=>1
001100000=>2
001100001=>1
001100010=>1
001100011=>0
001100100=>3
001100101=>2
001100110=>2
001100111=>1
001101000=>3
001101001=>2
001101010=>2
001101011=>1
001101100=>4
001101101=>3
001101110=>3
001101111=>2
001110000=>2
001110001=>1
001110010=>1
001110011=>0
001110100=>3
001110101=>2
001110110=>2
001110111=>1
001111000=>3
001111001=>2
001111010=>2
001111011=>1
001111100=>4
001111101=>3
001111110=>3
001111111=>2
010000000=>3
010000001=>2
010000010=>4
010000011=>3
010000100=>2
010000101=>1
010000110=>3
010000111=>2
010001000=>2
010001001=>1
010001010=>3
010001011=>2
010001100=>1
010001101=>0
010001110=>2
010001111=>1
010010000=>3
010010001=>2
010010010=>4
010010011=>3
010010100=>2
010010101=>1
010010110=>3
010010111=>2
010011000=>2
010011001=>1
010011010=>3
010011011=>2
010011100=>1
010011101=>0
010011110=>2
010011111=>1
010100000=>2
010100001=>1
010100010=>3
010100011=>2
010100100=>1
010100101=>0
010100110=>2
010100111=>1
010101000=>3
010101001=>2
010101010=>4
010101011=>3
010101100=>2
010101101=>1
010101110=>3
010101111=>2
010110000=>2
010110001=>1
010110010=>3
010110011=>2
010110100=>1
010110101=>0
010110110=>2
010110111=>1
010111000=>3
010111001=>2
010111010=>4
010111011=>3
010111100=>2
010111101=>1
010111110=>3
010111111=>2
011000000=>2
011000001=>1
011000010=>3
011000011=>2
011000100=>3
011000101=>2
011000110=>4
011000111=>3
011001000=>1
011001001=>0
011001010=>2
011001011=>1
011001100=>2
011001101=>1
011001110=>3
011001111=>2
011010000=>2
011010001=>1
011010010=>3
011010011=>2
011010100=>3
011010101=>2
011010110=>4
011010111=>3
011011000=>1
011011001=>0
011011010=>2
011011011=>1
011011100=>2
011011101=>1
011011110=>3
011011111=>2
011100000=>1
011100001=>0
011100010=>2
011100011=>1
011100100=>2
011100101=>1
011100110=>3
011100111=>2
011101000=>2
011101001=>1
011101010=>3
011101011=>2
011101100=>3
011101101=>2
011101110=>4
011101111=>3
011110000=>1
011110001=>0
011110010=>2
011110011=>1
011110100=>2
011110101=>1
011110110=>3
011110111=>2
011111000=>2
011111001=>1
011111010=>3
011111011=>2
011111100=>3
011111101=>2
011111110=>4
011111111=>3
100000000=>3
100000001=>4
100000010=>2
100000011=>3
100000100=>2
100000101=>3
100000110=>1
100000111=>2
100001000=>2
100001001=>3
100001010=>1
100001011=>2
100001100=>1
100001101=>2
100001110=>0
100001111=>1
100010000=>3
100010001=>4
100010010=>2
100010011=>3
100010100=>2
100010101=>3
100010110=>1
100010111=>2
100011000=>2
100011001=>3
100011010=>1
100011011=>2
100011100=>1
100011101=>2
100011110=>0
100011111=>1
100100000=>2
100100001=>3
100100010=>1
100100011=>2
100100100=>1
100100101=>2
100100110=>0
100100111=>1
100101000=>3
100101001=>4
100101010=>2
100101011=>3
100101100=>2
100101101=>3
100101110=>1
100101111=>2
100110000=>2
100110001=>3
100110010=>1
100110011=>2
100110100=>1
100110101=>2
100110110=>0
100110111=>1
100111000=>3
100111001=>4
100111010=>2
100111011=>3
100111100=>2
100111101=>3
100111110=>1
100111111=>2
101000000=>2
101000001=>3
101000010=>1
101000011=>2
101000100=>3
101000101=>4
101000110=>2
101000111=>3
101001000=>1
101001001=>2
101001010=>0
101001011=>1
101001100=>2
101001101=>3
101001110=>1
101001111=>2
101010000=>2
101010001=>3
101010010=>1
101010011=>2
101010100=>3
101010101=>4
101010110=>2
101010111=>3
101011000=>1
101011001=>2
101011010=>0
101011011=>1
101011100=>2
101011101=>3
101011110=>1
101011111=>2
101100000=>1
101100001=>2
101100010=>0
101100011=>1
101100100=>2
101100101=>3
101100110=>1
101100111=>2
101101000=>2
101101001=>3
101101010=>1
101101011=>2
101101100=>3
101101101=>4
101101110=>2
101101111=>3
101110000=>1
101110001=>2
101110010=>0
101110011=>1
101110100=>2
101110101=>3
101110110=>1
101110111=>2
101111000=>2
101111001=>3
101111010=>1
101111011=>2
101111100=>3
101111101=>4
101111110=>2
101111111=>3
110000000=>2
110000001=>3
110000010=>3
110000011=>4
110000100=>1
110000101=>2
110000110=>2
110000111=>3
110001000=>1
110001001=>2
110001010=>2
110001011=>3
110001100=>0
110001101=>1
110001110=>1
110001111=>2
110010000=>2
110010001=>3
110010010=>3
110010011=>4
110010100=>1
110010101=>2
110010110=>2
110010111=>3
110011000=>1
110011001=>2
110011010=>2
110011011=>3
110011100=>0
110011101=>1
110011110=>1
110011111=>2
110100000=>1
110100001=>2
110100010=>2
110100011=>3
110100100=>0
110100101=>1
110100110=>1
110100111=>2
110101000=>2
110101001=>3
110101010=>3
110101011=>4
110101100=>1
110101101=>2
110101110=>2
110101111=>3
110110000=>1
110110001=>2
110110010=>2
110110011=>3
110110100=>0
110110101=>1
110110110=>1
110110111=>2
110111000=>2
110111001=>3
110111010=>3
110111011=>4
110111100=>1
110111101=>2
110111110=>2
110111111=>3
111000000=>1
111000001=>2
111000010=>2
111000011=>3
111000100=>2
111000101=>3
111000110=>3
111000111=>4
111001000=>0
111001001=>1
111001010=>1
111001011=>2
111001100=>1
111001101=>2
111001110=>2
111001111=>3
111010000=>1
111010001=>2
111010010=>2
111010011=>3
111010100=>2
111010101=>3
111010110=>3
111010111=>4
111011000=>0
111011001=>1
111011010=>1
111011011=>2
111011100=>1
111011101=>2
111011110=>2
111011111=>3
111100000=>0
111100001=>1
111100010=>1
111100011=>2
111100100=>1
111100101=>2
111100110=>2
111100111=>3
111101000=>1
111101001=>2
111101010=>2
111101011=>3
111101100=>2
111101101=>3
111101110=>3
111101111=>4
111110000=>0
111110001=>1
111110010=>1
111110011=>2
111110100=>1
111110101=>2
111110110=>2
111110111=>3
111111000=>1
111111001=>2
111111010=>2
111111011=>3
111111100=>2
111111101=>3
111111110=>3
111111111=>4
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Description
The degree of symmetry of a binary word.
For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.
For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.
Code
def statistic(D): result = sum(1 for a, b in zip(D, D[::-1]) if a == b) if is_even(len(D)): return result/2 return (result-1)/2
Created
Mar 02, 2020 at 21:32 by Martin Rubey
Updated
Mar 02, 2020 at 21:32 by Martin Rubey
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