Identifier
- St000295: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>1
01=>0
10=>0
11=>1
000=>2
001=>0
010=>1
011=>0
100=>0
101=>1
110=>0
111=>2
0000=>3
0001=>0
0010=>1
0011=>0
0100=>1
0101=>2
0110=>1
0111=>0
1000=>0
1001=>1
1010=>2
1011=>1
1100=>0
1101=>1
1110=>0
1111=>3
00000=>4
00001=>0
00010=>1
00011=>0
00100=>2
00101=>0
00110=>1
00111=>0
01000=>1
01001=>2
01010=>3
01011=>0
01100=>1
01101=>2
01110=>1
01111=>0
10000=>0
10001=>1
10010=>2
10011=>1
10100=>0
10101=>3
10110=>2
10111=>1
11000=>0
11001=>1
11010=>0
11011=>2
11100=>0
11101=>1
11110=>0
11111=>4
000000=>5
000001=>0
000010=>1
000011=>0
000100=>2
000101=>0
000110=>1
000111=>0
001000=>2
001001=>3
001010=>1
001011=>0
001100=>2
001101=>0
001110=>1
001111=>0
010000=>1
010001=>2
010010=>3
010011=>0
010100=>1
010101=>4
010110=>1
010111=>0
011000=>1
011001=>2
011010=>1
011011=>3
011100=>1
011101=>2
011110=>1
011111=>0
100000=>0
100001=>1
100010=>2
100011=>1
100100=>3
100101=>1
100110=>2
100111=>1
101000=>0
101001=>1
101010=>4
101011=>1
101100=>0
101101=>3
101110=>2
101111=>1
110000=>0
110001=>1
110010=>0
110011=>2
110100=>0
110101=>1
110110=>3
110111=>2
111000=>0
111001=>1
111010=>0
111011=>2
111100=>0
111101=>1
111110=>0
111111=>5
0000000=>6
0000001=>0
0000010=>1
0000011=>0
0000100=>2
0000101=>0
0000110=>1
0000111=>0
0001000=>3
0001001=>0
0001010=>1
0001011=>0
0001100=>2
0001101=>0
0001110=>1
0001111=>0
0010000=>2
0010001=>3
0010010=>4
0010011=>0
0010100=>2
0010101=>0
0010110=>1
0010111=>0
0011000=>2
0011001=>3
0011010=>1
0011011=>0
0011100=>2
0011101=>0
0011110=>1
0011111=>0
0100000=>1
0100001=>2
0100010=>3
0100011=>0
0100100=>4
0100101=>2
0100110=>1
0100111=>0
0101000=>1
0101001=>2
0101010=>5
0101011=>0
0101100=>1
0101101=>2
0101110=>1
0101111=>0
0110000=>1
0110001=>2
0110010=>1
0110011=>3
0110100=>1
0110101=>2
0110110=>4
0110111=>0
0111000=>1
0111001=>2
0111010=>1
0111011=>3
0111100=>1
0111101=>2
0111110=>1
0111111=>0
1000000=>0
1000001=>1
1000010=>2
1000011=>1
1000100=>3
1000101=>1
1000110=>2
1000111=>1
1001000=>0
1001001=>4
1001010=>2
1001011=>1
1001100=>3
1001101=>1
1001110=>2
1001111=>1
1010000=>0
1010001=>1
1010010=>2
1010011=>1
1010100=>0
1010101=>5
1010110=>2
1010111=>1
1011000=>0
1011001=>1
1011010=>2
1011011=>4
1011100=>0
1011101=>3
1011110=>2
1011111=>1
1100000=>0
1100001=>1
1100010=>0
1100011=>2
1100100=>0
1100101=>1
1100110=>3
1100111=>2
1101000=>0
1101001=>1
1101010=>0
1101011=>2
1101100=>0
1101101=>4
1101110=>3
1101111=>2
1110000=>0
1110001=>1
1110010=>0
1110011=>2
1110100=>0
1110101=>1
1110110=>0
1110111=>3
1111000=>0
1111001=>1
1111010=>0
1111011=>2
1111100=>0
1111101=>1
1111110=>0
1111111=>6
00000000=>7
00000001=>0
00000010=>1
00000011=>0
00000100=>2
00000101=>0
00000110=>1
00000111=>0
00001000=>3
00001001=>0
00001010=>1
00001011=>0
00001100=>2
00001101=>0
00001110=>1
00001111=>0
00010000=>3
00010001=>4
00010010=>1
00010011=>0
00010100=>2
00010101=>0
00010110=>1
00010111=>0
00011000=>3
00011001=>0
00011010=>1
00011011=>0
00011100=>2
00011101=>0
00011110=>1
00011111=>0
00100000=>2
00100001=>3
00100010=>4
00100011=>0
00100100=>5
00100101=>0
00100110=>1
00100111=>0
00101000=>2
00101001=>3
00101010=>1
00101011=>0
00101100=>2
00101101=>0
00101110=>1
00101111=>0
00110000=>2
00110001=>3
00110010=>1
00110011=>4
00110100=>2
00110101=>0
00110110=>1
00110111=>0
00111000=>2
00111001=>3
00111010=>1
00111011=>0
00111100=>2
00111101=>0
00111110=>1
00111111=>0
01000000=>1
01000001=>2
01000010=>3
01000011=>0
01000100=>4
01000101=>2
01000110=>1
01000111=>0
01001000=>1
01001001=>5
01001010=>3
01001011=>0
01001100=>1
01001101=>2
01001110=>1
01001111=>0
01010000=>1
01010001=>2
01010010=>3
01010011=>0
01010100=>1
01010101=>6
01010110=>1
01010111=>0
01011000=>1
01011001=>2
01011010=>3
01011011=>0
01011100=>1
01011101=>2
01011110=>1
01011111=>0
01100000=>1
01100001=>2
01100010=>1
01100011=>3
01100100=>1
01100101=>2
01100110=>4
01100111=>0
01101000=>1
01101001=>2
01101010=>1
01101011=>3
01101100=>1
01101101=>5
01101110=>1
01101111=>0
01110000=>1
01110001=>2
01110010=>1
01110011=>3
01110100=>1
01110101=>2
01110110=>1
01110111=>4
01111000=>1
01111001=>2
01111010=>1
01111011=>3
01111100=>1
01111101=>2
01111110=>1
01111111=>0
10000000=>0
10000001=>1
10000010=>2
10000011=>1
10000100=>3
10000101=>1
10000110=>2
10000111=>1
10001000=>4
10001001=>1
10001010=>2
10001011=>1
10001100=>3
10001101=>1
10001110=>2
10001111=>1
10010000=>0
10010001=>1
10010010=>5
10010011=>1
10010100=>3
10010101=>1
10010110=>2
10010111=>1
10011000=>0
10011001=>4
10011010=>2
10011011=>1
10011100=>3
10011101=>1
10011110=>2
10011111=>1
10100000=>0
10100001=>1
10100010=>2
10100011=>1
10100100=>0
10100101=>3
10100110=>2
10100111=>1
10101000=>0
10101001=>1
10101010=>6
10101011=>1
10101100=>0
10101101=>3
10101110=>2
10101111=>1
10110000=>0
10110001=>1
10110010=>2
10110011=>1
10110100=>0
10110101=>3
10110110=>5
10110111=>1
10111000=>0
10111001=>1
10111010=>2
10111011=>4
10111100=>0
10111101=>3
10111110=>2
10111111=>1
11000000=>0
11000001=>1
11000010=>0
11000011=>2
11000100=>0
11000101=>1
11000110=>3
11000111=>2
11001000=>0
11001001=>1
11001010=>0
11001011=>2
11001100=>4
11001101=>1
11001110=>3
11001111=>2
11010000=>0
11010001=>1
11010010=>0
11010011=>2
11010100=>0
11010101=>1
11010110=>3
11010111=>2
11011000=>0
11011001=>1
11011010=>0
11011011=>5
11011100=>0
11011101=>4
11011110=>3
11011111=>2
11100000=>0
11100001=>1
11100010=>0
11100011=>2
11100100=>0
11100101=>1
11100110=>0
11100111=>3
11101000=>0
11101001=>1
11101010=>0
11101011=>2
11101100=>0
11101101=>1
11101110=>4
11101111=>3
11110000=>0
11110001=>1
11110010=>0
11110011=>2
11110100=>0
11110101=>1
11110110=>0
11110111=>3
11111000=>0
11111001=>1
11111010=>0
11111011=>2
11111100=>0
11111101=>1
11111110=>0
11111111=>7
000000000=>8
000000001=>0
000000010=>1
000000011=>0
000000100=>2
000000101=>0
000000110=>1
000000111=>0
000001000=>3
000001001=>0
000001010=>1
000001011=>0
000001100=>2
000001101=>0
000001110=>1
000001111=>0
000010000=>4
000010001=>0
000010010=>1
000010011=>0
000010100=>2
000010101=>0
000010110=>1
000010111=>0
000011000=>3
000011001=>0
000011010=>1
000011011=>0
000011100=>2
000011101=>0
000011110=>1
000011111=>0
000100000=>3
000100001=>4
000100010=>5
000100011=>0
000100100=>2
000100101=>0
000100110=>1
000100111=>0
000101000=>3
000101001=>0
000101010=>1
000101011=>0
000101100=>2
000101101=>0
000101110=>1
000101111=>0
000110000=>3
000110001=>4
000110010=>1
000110011=>0
000110100=>2
000110101=>0
000110110=>1
000110111=>0
000111000=>3
000111001=>0
000111010=>1
000111011=>0
000111100=>2
000111101=>0
000111110=>1
000111111=>0
001000000=>2
001000001=>3
001000010=>4
001000011=>0
001000100=>5
001000101=>0
001000110=>1
001000111=>0
001001000=>2
001001001=>6
001001010=>1
001001011=>0
001001100=>2
001001101=>0
001001110=>1
001001111=>0
001010000=>2
001010001=>3
001010010=>4
001010011=>0
001010100=>2
001010101=>0
001010110=>1
001010111=>0
001011000=>2
001011001=>3
001011010=>1
001011011=>0
001011100=>2
001011101=>0
001011110=>1
001011111=>0
001100000=>2
001100001=>3
001100010=>1
001100011=>4
001100100=>2
001100101=>0
001100110=>5
001100111=>0
001101000=>2
001101001=>3
001101010=>1
001101011=>0
001101100=>2
001101101=>0
001101110=>1
001101111=>0
001110000=>2
001110001=>3
001110010=>1
001110011=>4
001110100=>2
001110101=>0
001110110=>1
001110111=>0
001111000=>2
001111001=>3
001111010=>1
001111011=>0
001111100=>2
001111101=>0
001111110=>1
001111111=>0
010000000=>1
010000001=>2
010000010=>3
010000011=>0
010000100=>4
010000101=>2
010000110=>1
010000111=>0
010001000=>5
010001001=>2
010001010=>3
010001011=>0
010001100=>1
010001101=>2
010001110=>1
010001111=>0
010010000=>1
010010001=>2
010010010=>6
010010011=>0
010010100=>4
010010101=>2
010010110=>1
010010111=>0
010011000=>1
010011001=>2
010011010=>3
010011011=>0
010011100=>1
010011101=>2
010011110=>1
010011111=>0
010100000=>1
010100001=>2
010100010=>3
010100011=>0
010100100=>1
010100101=>4
010100110=>1
010100111=>0
010101000=>1
010101001=>2
010101010=>7
010101011=>0
010101100=>1
010101101=>2
010101110=>1
010101111=>0
010110000=>1
010110001=>2
010110010=>3
010110011=>0
010110100=>1
010110101=>4
010110110=>1
010110111=>0
010111000=>1
010111001=>2
010111010=>3
010111011=>0
010111100=>1
010111101=>2
010111110=>1
010111111=>0
011000000=>1
011000001=>2
011000010=>1
011000011=>3
011000100=>1
011000101=>2
011000110=>4
011000111=>0
011001000=>1
011001001=>2
011001010=>1
011001011=>3
011001100=>5
011001101=>2
011001110=>1
011001111=>0
011010000=>1
011010001=>2
011010010=>1
011010011=>3
011010100=>1
011010101=>2
011010110=>4
011010111=>0
011011000=>1
011011001=>2
011011010=>1
011011011=>6
011011100=>1
011011101=>2
011011110=>1
011011111=>0
011100000=>1
011100001=>2
011100010=>1
011100011=>3
011100100=>1
011100101=>2
011100110=>1
011100111=>4
011101000=>1
011101001=>2
011101010=>1
011101011=>3
011101100=>1
011101101=>2
011101110=>5
011101111=>0
011110000=>1
011110001=>2
011110010=>1
011110011=>3
011110100=>1
011110101=>2
011110110=>1
011110111=>4
011111000=>1
011111001=>2
011111010=>1
011111011=>3
011111100=>1
011111101=>2
011111110=>1
011111111=>0
100000000=>0
100000001=>1
100000010=>2
100000011=>1
100000100=>3
100000101=>1
100000110=>2
100000111=>1
100001000=>4
100001001=>1
100001010=>2
100001011=>1
100001100=>3
100001101=>1
100001110=>2
100001111=>1
100010000=>0
100010001=>5
100010010=>2
100010011=>1
100010100=>3
100010101=>1
100010110=>2
100010111=>1
100011000=>4
100011001=>1
100011010=>2
100011011=>1
100011100=>3
100011101=>1
100011110=>2
100011111=>1
100100000=>0
100100001=>1
100100010=>2
100100011=>1
100100100=>6
100100101=>1
100100110=>2
100100111=>1
100101000=>0
100101001=>4
100101010=>2
100101011=>1
100101100=>3
100101101=>1
100101110=>2
100101111=>1
100110000=>0
100110001=>1
100110010=>2
100110011=>5
100110100=>3
100110101=>1
100110110=>2
100110111=>1
100111000=>0
100111001=>4
100111010=>2
100111011=>1
100111100=>3
100111101=>1
100111110=>2
100111111=>1
101000000=>0
101000001=>1
101000010=>2
101000011=>1
101000100=>0
101000101=>3
101000110=>2
101000111=>1
101001000=>0
101001001=>1
101001010=>4
101001011=>1
101001100=>0
101001101=>3
101001110=>2
101001111=>1
101010000=>0
101010001=>1
101010010=>2
101010011=>1
101010100=>0
101010101=>7
101010110=>2
101010111=>1
101011000=>0
101011001=>1
101011010=>4
101011011=>1
101011100=>0
101011101=>3
101011110=>2
101011111=>1
101100000=>0
101100001=>1
101100010=>2
101100011=>1
101100100=>0
101100101=>3
101100110=>2
101100111=>1
101101000=>0
101101001=>1
101101010=>2
101101011=>4
101101100=>0
101101101=>6
101101110=>2
101101111=>1
101110000=>0
101110001=>1
101110010=>2
101110011=>1
101110100=>0
101110101=>3
101110110=>2
101110111=>5
101111000=>0
101111001=>1
101111010=>2
101111011=>4
101111100=>0
101111101=>3
101111110=>2
101111111=>1
110000000=>0
110000001=>1
110000010=>0
110000011=>2
110000100=>0
110000101=>1
110000110=>3
110000111=>2
110001000=>0
110001001=>1
110001010=>0
110001011=>2
110001100=>4
110001101=>1
110001110=>3
110001111=>2
110010000=>0
110010001=>1
110010010=>0
110010011=>2
110010100=>0
110010101=>1
110010110=>3
110010111=>2
110011000=>0
110011001=>5
110011010=>0
110011011=>2
110011100=>4
110011101=>1
110011110=>3
110011111=>2
110100000=>0
110100001=>1
110100010=>0
110100011=>2
110100100=>0
110100101=>1
110100110=>3
110100111=>2
110101000=>0
110101001=>1
110101010=>0
110101011=>2
110101100=>0
110101101=>4
110101110=>3
110101111=>2
110110000=>0
110110001=>1
110110010=>0
110110011=>2
110110100=>0
110110101=>1
110110110=>6
110110111=>2
110111000=>0
110111001=>1
110111010=>0
110111011=>5
110111100=>0
110111101=>4
110111110=>3
110111111=>2
111000000=>0
111000001=>1
111000010=>0
111000011=>2
111000100=>0
111000101=>1
111000110=>0
111000111=>3
111001000=>0
111001001=>1
111001010=>0
111001011=>2
111001100=>0
111001101=>1
111001110=>4
111001111=>3
111010000=>0
111010001=>1
111010010=>0
111010011=>2
111010100=>0
111010101=>1
111010110=>0
111010111=>3
111011000=>0
111011001=>1
111011010=>0
111011011=>2
111011100=>0
111011101=>5
111011110=>4
111011111=>3
111100000=>0
111100001=>1
111100010=>0
111100011=>2
111100100=>0
111100101=>1
111100110=>0
111100111=>3
111101000=>0
111101001=>1
111101010=>0
111101011=>2
111101100=>0
111101101=>1
111101110=>0
111101111=>4
111110000=>0
111110001=>1
111110010=>0
111110011=>2
111110100=>0
111110101=>1
111110110=>0
111110111=>3
111111000=>0
111111001=>1
111111010=>0
111111011=>2
111111100=>0
111111101=>1
111111110=>0
111111111=>8
0000000001=>0
0010000001=>3
0010101101=>0
0010101011=>0
0010100111=>0
0010011101=>0
0010011011=>0
0010010111=>0
0010001111=>0
0001110101=>0
0001110011=>0
0001101101=>0
0001101011=>0
0001100111=>0
0001011101=>0
0001011011=>0
0001010111=>0
0001001111=>0
0000111101=>0
0000111011=>0
0000110111=>0
0000101111=>0
0000011111=>0
0000000000=>9
0000000110=>1
0000011000=>3
0000011110=>1
0000010010=>1
0001100000=>3
0001100110=>1
0001111000=>3
0001111110=>1
0001110010=>1
0001001000=>3
0001001110=>1
0001000010=>5
0001011010=>1
0010101010=>1
0010101000=>2
0010101100=>2
0010100100=>2
0010010100=>2
0001010100=>2
0010101110=>1
0010100000=>2
0010000100=>5
0000010100=>2
0000000010=>1
0000001110=>1
0000111110=>1
0000000100=>2
0000001010=>1
0000010110=>1
0000101110=>1
0001011110=>1
0001101110=>1
0001110110=>1
0001111010=>1
0001111100=>2
0000000101=>0
0000001101=>0
0000011101=>0
0001111101=>0
0000001001=>0
0000010101=>0
0000101101=>0
0010110001=>3
0001100001=>4
0001000001=>4
0000111111=>0
0001110100=>2
0001101100=>2
0010011100=>2
0001011100=>2
0000111100=>2
0001101010=>1
0010011010=>1
0000111010=>1
0010100110=>1
0010010110=>1
0001010110=>1
0000110110=>1
0010001110=>1
0001101001=>0
0000110001=>0
0000010001=>0
0000001100=>2
0000011001=>0
0000110011=>0
0000110100=>2
0000000011=>0
0000011011=>0
0001101111=>0
0000110101=>0
0010000010=>4
0001000011=>0
0010011110=>1
0001010000=>3
0001000100=>6
0001010101=>0
0001001011=>0
0001100011=>5
0001110111=>0
0010000000=>2
0000000111=>0
0000001111=>0
0001111111=>0
0000001011=>0
0000010111=>0
0001011111=>0
0001111001=>0
0000011010=>1
0000101010=>1
0000100101=>0
0010010001=>3
0010000101=>0
0010010101=>0
0010010011=>0
0000101011=>0
0001000111=>0
0000100111=>0
0010010010=>7
0001001010=>1
0001001001=>0
0001000101=>0
0000100011=>0
0000100100=>2
0000100010=>1
0010110000=>2
0000011100=>2
0000001000=>3
0000101100=>2
0010101111=>0
0000101000=>3
0010001000=>6
0001001100=>2
0001000110=>1
0001100100=>2
0001100010=>1
0000100110=>1
0000110010=>1
0010010000=>2
0001010010=>1
0001000000=>3
0001011001=>0
0001100101=>0
0001110001=>4
0010011001=>3
0010100101=>5
0010101001=>3
0010011111=>0
0000111001=>0
0010001101=>0
0001001101=>0
0001010001=>4
0001010011=>0
0001111011=>0
0010011000=>2
0001011000=>3
0000100000=>4
0010001011=>0
0010000111=>0
0000010011=>0
0010001100=>2
0010000110=>1
0000110000=>4
0000100001=>5
0010100011=>0
0010100001=>3
0000111000=>3
0001101000=>3
0000010000=>4
0000101001=>0
0010100010=>4
0010001001=>3
0010000011=>0
0010001010=>1
0001110000=>3
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The length of the border of a binary word.
The border of a word is the longest word which is both a proper prefix and a proper suffix, including a possible empty border.
The border of a word is the longest word which is both a proper prefix and a proper suffix, including a possible empty border.
Code
def statistic(x): return x.length_border()
Created
Nov 19, 2015 at 12:22 by Martin Rubey
Updated
Nov 19, 2015 at 12:53 by Christian Stump
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