Identifier
- St000626: Binary words ⟶ ℤ
Values
=>
0=>1
1=>1
00=>1
01=>2
10=>2
11=>1
000=>1
001=>3
010=>2
011=>3
100=>3
101=>2
110=>3
111=>1
0000=>1
0001=>4
0010=>3
0011=>4
0100=>3
0101=>2
0110=>3
0111=>4
1000=>4
1001=>3
1010=>2
1011=>3
1100=>4
1101=>3
1110=>4
1111=>1
00000=>1
00001=>5
00010=>4
00011=>5
00100=>3
00101=>5
00110=>4
00111=>5
01000=>4
01001=>3
01010=>2
01011=>5
01100=>4
01101=>3
01110=>4
01111=>5
10000=>5
10001=>4
10010=>3
10011=>4
10100=>5
10101=>2
10110=>3
10111=>4
11000=>5
11001=>4
11010=>5
11011=>3
11100=>5
11101=>4
11110=>5
11111=>1
000000=>1
000001=>6
000010=>5
000011=>6
000100=>4
000101=>6
000110=>5
000111=>6
001000=>4
001001=>3
001010=>5
001011=>6
001100=>4
001101=>6
001110=>5
001111=>6
010000=>5
010001=>4
010010=>3
010011=>6
010100=>5
010101=>2
010110=>5
010111=>6
011000=>5
011001=>4
011010=>5
011011=>3
011100=>5
011101=>4
011110=>5
011111=>6
100000=>6
100001=>5
100010=>4
100011=>5
100100=>3
100101=>5
100110=>4
100111=>5
101000=>6
101001=>5
101010=>2
101011=>5
101100=>6
101101=>3
101110=>4
101111=>5
110000=>6
110001=>5
110010=>6
110011=>4
110100=>6
110101=>5
110110=>3
110111=>4
111000=>6
111001=>5
111010=>6
111011=>4
111100=>6
111101=>5
111110=>6
111111=>1
0000000=>1
0000001=>7
0000010=>6
0000011=>7
0000100=>5
0000101=>7
0000110=>6
0000111=>7
0001000=>4
0001001=>7
0001010=>6
0001011=>7
0001100=>5
0001101=>7
0001110=>6
0001111=>7
0010000=>5
0010001=>4
0010010=>3
0010011=>7
0010100=>5
0010101=>7
0010110=>6
0010111=>7
0011000=>5
0011001=>4
0011010=>6
0011011=>7
0011100=>5
0011101=>7
0011110=>6
0011111=>7
0100000=>6
0100001=>5
0100010=>4
0100011=>7
0100100=>3
0100101=>5
0100110=>6
0100111=>7
0101000=>6
0101001=>5
0101010=>2
0101011=>7
0101100=>6
0101101=>5
0101110=>6
0101111=>7
0110000=>6
0110001=>5
0110010=>6
0110011=>4
0110100=>6
0110101=>5
0110110=>3
0110111=>7
0111000=>6
0111001=>5
0111010=>6
0111011=>4
0111100=>6
0111101=>5
0111110=>6
0111111=>7
1000000=>7
1000001=>6
1000010=>5
1000011=>6
1000100=>4
1000101=>6
1000110=>5
1000111=>6
1001000=>7
1001001=>3
1001010=>5
1001011=>6
1001100=>4
1001101=>6
1001110=>5
1001111=>6
1010000=>7
1010001=>6
1010010=>5
1010011=>6
1010100=>7
1010101=>2
1010110=>5
1010111=>6
1011000=>7
1011001=>6
1011010=>5
1011011=>3
1011100=>7
1011101=>4
1011110=>5
1011111=>6
1100000=>7
1100001=>6
1100010=>7
1100011=>5
1100100=>7
1100101=>6
1100110=>4
1100111=>5
1101000=>7
1101001=>6
1101010=>7
1101011=>5
1101100=>7
1101101=>3
1101110=>4
1101111=>5
1110000=>7
1110001=>6
1110010=>7
1110011=>5
1110100=>7
1110101=>6
1110110=>7
1110111=>4
1111000=>7
1111001=>6
1111010=>7
1111011=>5
1111100=>7
1111101=>6
1111110=>7
1111111=>1
00000000=>1
00000001=>8
00000010=>7
00000011=>8
00000100=>6
00000101=>8
00000110=>7
00000111=>8
00001000=>5
00001001=>8
00001010=>7
00001011=>8
00001100=>6
00001101=>8
00001110=>7
00001111=>8
00010000=>5
00010001=>4
00010010=>7
00010011=>8
00010100=>6
00010101=>8
00010110=>7
00010111=>8
00011000=>5
00011001=>8
00011010=>7
00011011=>8
00011100=>6
00011101=>8
00011110=>7
00011111=>8
00100000=>6
00100001=>5
00100010=>4
00100011=>8
00100100=>3
00100101=>8
00100110=>7
00100111=>8
00101000=>6
00101001=>5
00101010=>7
00101011=>8
00101100=>6
00101101=>8
00101110=>7
00101111=>8
00110000=>6
00110001=>5
00110010=>7
00110011=>4
00110100=>6
00110101=>8
00110110=>7
00110111=>8
00111000=>6
00111001=>5
00111010=>7
00111011=>8
00111100=>6
00111101=>8
00111110=>7
00111111=>8
01000000=>7
01000001=>6
01000010=>5
01000011=>8
01000100=>4
01000101=>6
01000110=>7
01000111=>8
01001000=>7
01001001=>3
01001010=>5
01001011=>8
01001100=>7
01001101=>6
01001110=>7
01001111=>8
01010000=>7
01010001=>6
01010010=>5
01010011=>8
01010100=>7
01010101=>2
01010110=>7
01010111=>8
01011000=>7
01011001=>6
01011010=>5
01011011=>8
01011100=>7
01011101=>6
01011110=>7
01011111=>8
01100000=>7
01100001=>6
01100010=>7
01100011=>5
01100100=>7
01100101=>6
01100110=>4
01100111=>8
01101000=>7
01101001=>6
01101010=>7
01101011=>5
01101100=>7
01101101=>3
01101110=>7
01101111=>8
01110000=>7
01110001=>6
01110010=>7
01110011=>5
01110100=>7
01110101=>6
01110110=>7
01110111=>4
01111000=>7
01111001=>6
01111010=>7
01111011=>5
01111100=>7
01111101=>6
01111110=>7
01111111=>8
10000000=>8
10000001=>7
10000010=>6
10000011=>7
10000100=>5
10000101=>7
10000110=>6
10000111=>7
10001000=>4
10001001=>7
10001010=>6
10001011=>7
10001100=>5
10001101=>7
10001110=>6
10001111=>7
10010000=>8
10010001=>7
10010010=>3
10010011=>7
10010100=>5
10010101=>7
10010110=>6
10010111=>7
10011000=>8
10011001=>4
10011010=>6
10011011=>7
10011100=>5
10011101=>7
10011110=>6
10011111=>7
10100000=>8
10100001=>7
10100010=>6
10100011=>7
10100100=>8
10100101=>5
10100110=>6
10100111=>7
10101000=>8
10101001=>7
10101010=>2
10101011=>7
10101100=>8
10101101=>5
10101110=>6
10101111=>7
10110000=>8
10110001=>7
10110010=>6
10110011=>7
10110100=>8
10110101=>5
10110110=>3
10110111=>7
10111000=>8
10111001=>7
10111010=>6
10111011=>4
10111100=>8
10111101=>5
10111110=>6
10111111=>7
11000000=>8
11000001=>7
11000010=>8
11000011=>6
11000100=>8
11000101=>7
11000110=>5
11000111=>6
11001000=>8
11001001=>7
11001010=>8
11001011=>6
11001100=>4
11001101=>7
11001110=>5
11001111=>6
11010000=>8
11010001=>7
11010010=>8
11010011=>6
11010100=>8
11010101=>7
11010110=>5
11010111=>6
11011000=>8
11011001=>7
11011010=>8
11011011=>3
11011100=>8
11011101=>4
11011110=>5
11011111=>6
11100000=>8
11100001=>7
11100010=>8
11100011=>6
11100100=>8
11100101=>7
11100110=>8
11100111=>5
11101000=>8
11101001=>7
11101010=>8
11101011=>6
11101100=>8
11101101=>7
11101110=>4
11101111=>5
11110000=>8
11110001=>7
11110010=>8
11110011=>6
11110100=>8
11110101=>7
11110110=>8
11110111=>5
11111000=>8
11111001=>7
11111010=>8
11111011=>6
11111100=>8
11111101=>7
11111110=>8
11111111=>1
000000000=>1
000000001=>9
000000010=>8
000000011=>9
000000100=>7
000000101=>9
000000110=>8
000000111=>9
000001000=>6
000001001=>9
000001010=>8
000001011=>9
000001100=>7
000001101=>9
000001110=>8
000001111=>9
000010000=>5
000010001=>9
000010010=>8
000010011=>9
000010100=>7
000010101=>9
000010110=>8
000010111=>9
000011000=>6
000011001=>9
000011010=>8
000011011=>9
000011100=>7
000011101=>9
000011110=>8
000011111=>9
000100000=>6
000100001=>5
000100010=>4
000100011=>9
000100100=>7
000100101=>9
000100110=>8
000100111=>9
000101000=>6
000101001=>9
000101010=>8
000101011=>9
000101100=>7
000101101=>9
000101110=>8
000101111=>9
000110000=>6
000110001=>5
000110010=>8
000110011=>9
000110100=>7
000110101=>9
000110110=>8
000110111=>9
000111000=>6
000111001=>9
000111010=>8
000111011=>9
000111100=>7
000111101=>9
000111110=>8
000111111=>9
001000000=>7
001000001=>6
001000010=>5
001000011=>9
001000100=>4
001000101=>9
001000110=>8
001000111=>9
001001000=>7
001001001=>3
001001010=>8
001001011=>9
001001100=>7
001001101=>9
001001110=>8
001001111=>9
001010000=>7
001010001=>6
001010010=>5
001010011=>9
001010100=>7
001010101=>9
001010110=>8
001010111=>9
001011000=>7
001011001=>6
001011010=>8
001011011=>9
001011100=>7
001011101=>9
001011110=>8
001011111=>9
001100000=>7
001100001=>6
001100010=>8
001100011=>5
001100100=>7
001100101=>9
001100110=>4
001100111=>9
001101000=>7
001101001=>6
001101010=>8
001101011=>9
001101100=>7
001101101=>9
001101110=>8
001101111=>9
001110000=>7
001110001=>6
001110010=>8
001110011=>5
001110100=>7
001110101=>9
001110110=>8
001110111=>9
001111000=>7
001111001=>6
001111010=>8
001111011=>9
001111100=>7
001111101=>9
001111110=>8
001111111=>9
010000000=>8
010000001=>7
010000010=>6
010000011=>9
010000100=>5
010000101=>7
010000110=>8
010000111=>9
010001000=>4
010001001=>7
010001010=>6
010001011=>9
010001100=>8
010001101=>7
010001110=>8
010001111=>9
010010000=>8
010010001=>7
010010010=>3
010010011=>9
010010100=>5
010010101=>7
010010110=>8
010010111=>9
010011000=>8
010011001=>7
010011010=>6
010011011=>9
010011100=>8
010011101=>7
010011110=>8
010011111=>9
010100000=>8
010100001=>7
010100010=>6
010100011=>9
010100100=>8
010100101=>5
010100110=>8
010100111=>9
010101000=>8
010101001=>7
010101010=>2
010101011=>9
010101100=>8
010101101=>7
010101110=>8
010101111=>9
010110000=>8
010110001=>7
010110010=>6
010110011=>9
010110100=>8
010110101=>5
010110110=>8
010110111=>9
010111000=>8
010111001=>7
010111010=>6
010111011=>9
010111100=>8
010111101=>7
010111110=>8
010111111=>9
011000000=>8
011000001=>7
011000010=>8
011000011=>6
011000100=>8
011000101=>7
011000110=>5
011000111=>9
011001000=>8
011001001=>7
011001010=>8
011001011=>6
011001100=>4
011001101=>7
011001110=>8
011001111=>9
011010000=>8
011010001=>7
011010010=>8
011010011=>6
011010100=>8
011010101=>7
011010110=>5
011010111=>9
011011000=>8
011011001=>7
011011010=>8
011011011=>3
011011100=>8
011011101=>7
011011110=>8
011011111=>9
011100000=>8
011100001=>7
011100010=>8
011100011=>6
011100100=>8
011100101=>7
011100110=>8
011100111=>5
011101000=>8
011101001=>7
011101010=>8
011101011=>6
011101100=>8
011101101=>7
011101110=>4
011101111=>9
011110000=>8
011110001=>7
011110010=>8
011110011=>6
011110100=>8
011110101=>7
011110110=>8
011110111=>5
011111000=>8
011111001=>7
011111010=>8
011111011=>6
011111100=>8
011111101=>7
011111110=>8
011111111=>9
100000000=>9
100000001=>8
100000010=>7
100000011=>8
100000100=>6
100000101=>8
100000110=>7
100000111=>8
100001000=>5
100001001=>8
100001010=>7
100001011=>8
100001100=>6
100001101=>8
100001110=>7
100001111=>8
100010000=>9
100010001=>4
100010010=>7
100010011=>8
100010100=>6
100010101=>8
100010110=>7
100010111=>8
100011000=>5
100011001=>8
100011010=>7
100011011=>8
100011100=>6
100011101=>8
100011110=>7
100011111=>8
100100000=>9
100100001=>8
100100010=>7
100100011=>8
100100100=>3
100100101=>8
100100110=>7
100100111=>8
100101000=>9
100101001=>5
100101010=>7
100101011=>8
100101100=>6
100101101=>8
100101110=>7
100101111=>8
100110000=>9
100110001=>8
100110010=>7
100110011=>4
100110100=>6
100110101=>8
100110110=>7
100110111=>8
100111000=>9
100111001=>5
100111010=>7
100111011=>8
100111100=>6
100111101=>8
100111110=>7
100111111=>8
101000000=>9
101000001=>8
101000010=>7
101000011=>8
101000100=>9
101000101=>6
101000110=>7
101000111=>8
101001000=>9
101001001=>8
101001010=>5
101001011=>8
101001100=>9
101001101=>6
101001110=>7
101001111=>8
101010000=>9
101010001=>8
101010010=>7
101010011=>8
101010100=>9
101010101=>2
101010110=>7
101010111=>8
101011000=>9
101011001=>8
101011010=>5
101011011=>8
101011100=>9
101011101=>6
101011110=>7
101011111=>8
101100000=>9
101100001=>8
101100010=>7
101100011=>8
101100100=>9
101100101=>6
101100110=>7
101100111=>8
101101000=>9
101101001=>8
101101010=>7
101101011=>5
101101100=>9
101101101=>3
101101110=>7
101101111=>8
101110000=>9
101110001=>8
101110010=>7
101110011=>8
101110100=>9
101110101=>6
101110110=>7
101110111=>4
101111000=>9
101111001=>8
101111010=>7
101111011=>5
101111100=>9
101111101=>6
101111110=>7
101111111=>8
110000000=>9
110000001=>8
110000010=>9
110000011=>7
110000100=>9
110000101=>8
110000110=>6
110000111=>7
110001000=>9
110001001=>8
110001010=>9
110001011=>7
110001100=>5
110001101=>8
110001110=>6
110001111=>7
110010000=>9
110010001=>8
110010010=>9
110010011=>7
110010100=>9
110010101=>8
110010110=>6
110010111=>7
110011000=>9
110011001=>4
110011010=>9
110011011=>7
110011100=>5
110011101=>8
110011110=>6
110011111=>7
110100000=>9
110100001=>8
110100010=>9
110100011=>7
110100100=>9
110100101=>8
110100110=>6
110100111=>7
110101000=>9
110101001=>8
110101010=>9
110101011=>7
110101100=>9
110101101=>5
110101110=>6
110101111=>7
110110000=>9
110110001=>8
110110010=>9
110110011=>7
110110100=>9
110110101=>8
110110110=>3
110110111=>7
110111000=>9
110111001=>8
110111010=>9
110111011=>4
110111100=>9
110111101=>5
110111110=>6
110111111=>7
111000000=>9
111000001=>8
111000010=>9
111000011=>7
111000100=>9
111000101=>8
111000110=>9
111000111=>6
111001000=>9
111001001=>8
111001010=>9
111001011=>7
111001100=>9
111001101=>8
111001110=>5
111001111=>6
111010000=>9
111010001=>8
111010010=>9
111010011=>7
111010100=>9
111010101=>8
111010110=>9
111010111=>6
111011000=>9
111011001=>8
111011010=>9
111011011=>7
111011100=>9
111011101=>4
111011110=>5
111011111=>6
111100000=>9
111100001=>8
111100010=>9
111100011=>7
111100100=>9
111100101=>8
111100110=>9
111100111=>6
111101000=>9
111101001=>8
111101010=>9
111101011=>7
111101100=>9
111101101=>8
111101110=>9
111101111=>5
111110000=>9
111110001=>8
111110010=>9
111110011=>7
111110100=>9
111110101=>8
111110110=>9
111110111=>6
111111000=>9
111111001=>8
111111010=>9
111111011=>7
111111100=>9
111111101=>8
111111110=>9
111111111=>1
0000000001=>10
0010000001=>7
0010101101=>10
0010101011=>10
0010100111=>10
0010011101=>10
0010011011=>10
0010010111=>10
0010001111=>10
0001110101=>10
0001110011=>10
0001101101=>10
0001101011=>10
0001100111=>10
0001011101=>10
0001011011=>10
0001010111=>10
0001001111=>10
0000111101=>10
0000111011=>10
0000110111=>10
0000101111=>10
0000011111=>10
0000000000=>1
0000000110=>9
0000011000=>7
0000011110=>9
0000010010=>9
0001100000=>7
0001100110=>9
0001111000=>7
0001111110=>9
0001110010=>9
0001001000=>7
0001001110=>9
0001000010=>5
0001011010=>9
0010101010=>9
0010101000=>8
0010101100=>8
0010100100=>8
0010010100=>8
0001010100=>8
0010101110=>9
0010100000=>8
0010000100=>5
0000010100=>8
0000000010=>9
0000001110=>9
0000111110=>9
0000000100=>8
0000001010=>9
0000010110=>9
0000101110=>9
0001011110=>9
0001101110=>9
0001110110=>9
0001111010=>9
0001111100=>8
0000000101=>10
0000001101=>10
0000011101=>10
0001111101=>10
0000001001=>10
0000010101=>10
0000101101=>10
0010110001=>7
0001100001=>6
0001000001=>6
0000111111=>10
0001110100=>8
0001101100=>8
0010011100=>8
0001011100=>8
0000111100=>8
0001101010=>9
0010011010=>9
0000111010=>9
0010100110=>9
0010010110=>9
0001010110=>9
0000110110=>9
0010001110=>9
0001101001=>10
0000110001=>10
0000010001=>10
0000001100=>8
0000011001=>10
0000110011=>10
0000110100=>8
0000000011=>10
0000011011=>10
0001101111=>10
0000110101=>10
0010000010=>6
0001000011=>10
0010011110=>9
0001010000=>7
0001000100=>4
0001010101=>10
0001001011=>10
0001100011=>5
0001110111=>10
0010000000=>8
0000000111=>10
0000001111=>10
0001111111=>10
0000001011=>10
0000010111=>10
0001011111=>10
0001111001=>10
0000011010=>9
0000101010=>9
0000100101=>10
0010010001=>7
0010000101=>10
0010010101=>10
0010010011=>10
0000101011=>10
0001000111=>10
0000100111=>10
0010010010=>3
0001001010=>9
0001001001=>10
0001000101=>10
0000100011=>10
0000100100=>8
0000100010=>9
0010110000=>8
0000011100=>8
0000001000=>7
0000101100=>8
0010101111=>10
0000101000=>7
0010001000=>4
0001001100=>8
0001000110=>9
0001100100=>8
0001100010=>9
0000100110=>9
0000110010=>9
0010010000=>8
0001010010=>9
0001000000=>7
0001011001=>10
0001100101=>10
0001110001=>6
0010011001=>7
0010100101=>5
0010101001=>7
0010011111=>10
0000111001=>10
0010001101=>10
0001001101=>10
0001010001=>6
0001010011=>10
0001111011=>10
0010011000=>8
0001011000=>7
0000100000=>6
0010001011=>10
0010000111=>10
0000010011=>10
0010001100=>8
0010000110=>9
0000110000=>6
0000100001=>5
0010100011=>10
0010100001=>7
0000111000=>7
0001101000=>7
0000010000=>6
0000101001=>10
0010100010=>6
0010001001=>7
0010000011=>10
0010001010=>9
0001110000=>7
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 minimal period of a binary word.
This is the smallest natural number $p$ such that $w_i=w_{i+p}$ for all $i\in\{1,\dots,|w|-p\}$.
This is the smallest natural number $p$ such that $w_i=w_{i+p}$ for all $i\in\{1,\dots,|w|-p\}$.
Code
def statistic(w):
return w.minimal_period()
Created
Oct 16, 2016 at 22:07 by Martin Rubey
Updated
Oct 16, 2016 at 22:07 by Martin Rubey
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