Identifier
- St001424: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>1
01=>0
10=>0
11=>1
000=>1
001=>1
010=>0
011=>1
100=>1
101=>0
110=>1
111=>1
0000=>2
0001=>1
0010=>1
0011=>2
0100=>1
0101=>1
0110=>1
0111=>1
1000=>1
1001=>1
1010=>1
1011=>1
1100=>2
1101=>1
1110=>1
1111=>2
00000=>2
00001=>2
00010=>1
00011=>2
00100=>1
00101=>2
00110=>2
00111=>2
01000=>1
01001=>1
01010=>2
01011=>2
01100=>2
01101=>1
01110=>1
01111=>2
10000=>2
10001=>1
10010=>1
10011=>2
10100=>2
10101=>2
10110=>1
10111=>1
11000=>2
11001=>2
11010=>2
11011=>1
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11101=>1
11110=>2
11111=>2
000000=>3
000001=>2
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000100=>1
000101=>2
000110=>2
000111=>2
001000=>1
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001011=>3
001100=>2
001101=>2
001110=>2
001111=>3
010000=>2
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010100=>3
010101=>2
010110=>2
010111=>2
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011111=>2
100000=>2
100001=>2
100010=>1
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100100=>2
100101=>2
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101000=>2
101001=>2
101010=>2
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101101=>2
101110=>1
101111=>2
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110001=>2
110010=>2
110011=>2
110100=>3
110101=>3
110110=>2
110111=>1
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111001=>2
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111100=>3
111101=>2
111110=>2
111111=>3
0000000=>3
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1000000=>3
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1101010=>3
1101011=>3
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1101101=>3
1101110=>1
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1110000=>3
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1110111=>1
1111000=>3
1111001=>3
1111010=>3
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1111111=>3
00000000=>4
00000001=>3
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11011101=>2
11011110=>2
11011111=>2
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11100001=>3
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11110000=>4
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11111001=>3
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11111011=>2
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11111111=>4
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100010011=>3
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100010101=>3
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100011010=>3
100011011=>3
100011100=>2
100011101=>2
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100100011=>3
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111000011=>3
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111100000=>4
111100001=>4
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111100101=>4
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111100111=>3
111101000=>4
111101001=>4
111101010=>4
111101011=>4
111101100=>4
111101101=>4
111101110=>3
111101111=>2
111110000=>4
111110001=>3
111110010=>3
111110011=>3
111110100=>4
111110101=>4
111110110=>3
111110111=>2
111111000=>4
111111001=>4
111111010=>4
111111011=>3
111111100=>4
111111101=>3
111111110=>4
111111111=>4
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Description
The number of distinct squares in a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uu$ is a factor of the word.
Note that every word of length at least four contains a square.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uu$ is a factor of the word.
Note that every word of length at least four contains a square.
Code
def statistic(w): lst = [] for i in range(len(w)): for l in range(1, (len(w)-i)//2+1): if w[i:i+l] == w[i+l:i+2*l]: lst.append(tuple(w[i:i+l])) return len(set(lst))
Created
Jun 20, 2019 at 00:28 by Martin Rubey
Updated
Jun 20, 2019 at 08:39 by Martin Rubey
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