- FindStat

Identifier

St001417: Binary words ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        0=>1
1=>1
00=>2
01=>1
10=>1
11=>2
000=>3
001=>2
010=>3
011=>2
100=>2
101=>3
110=>2
111=>3
0000=>4
0001=>3
0010=>3
0011=>2
0100=>3
0101=>3
0110=>4
0111=>3
1000=>3
1001=>4
1010=>3
1011=>3
1100=>2
1101=>3
1110=>3
1111=>4
00000=>5
00001=>4
00010=>4
00011=>3
00100=>5
00101=>3
00110=>4
00111=>3
01000=>4
01001=>4
01010=>5
01011=>3
01100=>4
01101=>4
01110=>5
01111=>4
10000=>4
10001=>5
10010=>4
10011=>4
10100=>3
10101=>5
10110=>4
10111=>4
11000=>3
11001=>4
11010=>3
11011=>5
11100=>3
11101=>4
11110=>4
11111=>5
000000=>6
000001=>5
000010=>5
000011=>4
000100=>5
000101=>4
000110=>4
000111=>3
001000=>5
001001=>5
001010=>5
001011=>3
001100=>6
001101=>4
001110=>5
001111=>4
010000=>5
010001=>5
010010=>6
010011=>4
010100=>5
010101=>5
010110=>5
010111=>4
011000=>4
011001=>4
011010=>5
011011=>5
011100=>5
011101=>5
011110=>6
011111=>5
100000=>5
100001=>6
100010=>5
100011=>5
100100=>5
100101=>5
100110=>4
100111=>4
101000=>4
101001=>5
101010=>5
101011=>5
101100=>4
101101=>6
101110=>5
101111=>5
110000=>4
110001=>5
110010=>4
110011=>6
110100=>3
110101=>5
110110=>5
110111=>5
111000=>3
111001=>4
111010=>4
111011=>5
111100=>4
111101=>5
111110=>5
111111=>6
0000000=>7
0000001=>6
0000010=>6
0000011=>5
0000100=>6
0000101=>5
0000110=>5
0000111=>4
0001000=>7
0001001=>5
0001010=>5
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0001101=>4
0001110=>5
0001111=>4
0010000=>6
0010001=>5
0010010=>6
0010011=>5
0010100=>7
0010101=>5
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0010111=>4
0011000=>6
0011001=>6
0011010=>6
0011011=>5
0011100=>7
0011101=>5
0011110=>6
0011111=>5
0100000=>6
0100001=>6
0100010=>7
0100011=>5
0100100=>6
0100101=>6
0100110=>6
0100111=>4
0101000=>5
0101001=>5
0101010=>7
0101011=>5
0101100=>6
0101101=>6
0101110=>6
0101111=>5
0110000=>5
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0110010=>6
0110011=>6
0110100=>5
0110101=>5
0110110=>7
0110111=>5
0111000=>5
0111001=>5
0111010=>6
0111011=>5
0111100=>6
0111101=>6
0111110=>7
0111111=>6
1000000=>6
1000001=>7
1000010=>6
1000011=>6
1000100=>5
1000101=>6
1000110=>5
1000111=>5
1001000=>5
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1001010=>5
1001011=>5
1001100=>6
1001101=>6
1001110=>5
1001111=>5
1010000=>5
1010001=>6
1010010=>6
1010011=>6
1010100=>5
1010101=>7
1010110=>5
1010111=>5
1011000=>4
1011001=>6
1011010=>6
1011011=>6
1011100=>5
1011101=>7
1011110=>6
1011111=>6
1100000=>5
1100001=>6
1100010=>5
1100011=>7
1100100=>5
1100101=>6
1100110=>6
1100111=>6
1101000=>4
1101001=>5
1101010=>5
1101011=>7
1101100=>5
1101101=>6
1101110=>5
1101111=>6
1110000=>4
1110001=>5
1110010=>4
1110011=>6
1110100=>4
1110101=>5
1110110=>5
1110111=>7
1111000=>4
1111001=>5
1111010=>5
1111011=>6
1111100=>5
1111101=>6
1111110=>6
1111111=>7
00000000=>8
00000001=>7
00000010=>7
00000011=>6
00000100=>7
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00000110=>6
00000111=>5
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00001010=>6
00001011=>5
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00001111=>4
00010000=>7
00010001=>7
00010010=>7
00010011=>5
00010100=>7
00010101=>5
00010110=>5
00010111=>4
00011000=>8
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00011010=>6
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00011110=>6
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00100000=>7
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00100010=>7
00100011=>5
00100100=>8
00100101=>6
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00101000=>7
00101001=>7
00101010=>7
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00101100=>7
00101101=>6
00101110=>6
00101111=>5
00110000=>6
00110001=>6
00110010=>6
00110011=>6
00110100=>7
00110101=>6
00110110=>7
00110111=>5
00111000=>7
00111001=>7
00111010=>7
00111011=>5
00111100=>8
00111101=>6
00111110=>7
00111111=>6
01000000=>7
01000001=>7
01000010=>8
01000011=>6
01000100=>7
01000101=>7
01000110=>7
01000111=>5
01001000=>7
01001001=>7
01001010=>7
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01001100=>6
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01001110=>6
01001111=>5
01010000=>6
01010001=>6
01010010=>7
01010011=>6
01010100=>7
01010101=>7
01010110=>7
01010111=>5
01011000=>6
01011001=>6
01011010=>8
01011011=>6
01011100=>7
01011101=>7
01011110=>7
01011111=>6
01100000=>6
01100001=>6
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01100101=>6
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01101101=>7
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01110100=>6
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01111000=>6
01111001=>6
01111010=>7
01111011=>6
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01111111=>7
10000000=>7
10000001=>8
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10000101=>7
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10000111=>6
10001000=>7
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10001011=>6
10001100=>6
10001101=>6
10001110=>5
10001111=>5
10010000=>6
10010001=>7
10010010=>7
10010011=>7
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10011001=>8
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10011100=>7
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10011110=>6
10011111=>6
10100000=>6
10100001=>7
10100010=>7
10100011=>7
10100100=>6
10100101=>8
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10100111=>6
10101000=>5
10101001=>7
10101010=>7
10101011=>7
10101100=>6
10101101=>7
10101110=>6
10101111=>6
10110000=>5
10110001=>6
10110010=>6
10110011=>6
10110100=>6
10110101=>7
10110110=>7
10110111=>7
10111000=>5
10111001=>7
10111010=>7
10111011=>7
10111100=>6
10111101=>8
10111110=>7
10111111=>7
11000000=>6
11000001=>7
11000010=>6
11000011=>8
11000100=>5
11000101=>7
11000110=>7
11000111=>7
11001000=>5
11001001=>7
11001010=>6
11001011=>7
11001100=>6
11001101=>6
11001110=>6
11001111=>6
11010000=>5
11010001=>6
11010010=>6
11010011=>7
11010100=>5
11010101=>7
11010110=>7
11010111=>7
11011000=>5
11011001=>6
11011010=>6
11011011=>8
11011100=>5
11011101=>7
11011110=>6
11011111=>7
11100000=>5
11100001=>6
11100010=>5
11100011=>7
11100100=>5
11100101=>6
11100110=>6
11100111=>8
11101000=>4
11101001=>5
11101010=>5
11101011=>7
11101100=>5
11101101=>7
11101110=>7
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=>9
000000001=>8
000000010=>8
000000011=>7
000000100=>8
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000000110=>7
000000111=>6
000001000=>8
000001001=>7
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000001100=>7
000001101=>6
000001110=>6
000001111=>5
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001000000=>8
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001000010=>8
001000011=>6
001000100=>9
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001001001=>8
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001001110=>6
001001111=>5
001010000=>7
001010001=>7
001010010=>7
001010011=>7
001010100=>9
001010101=>7
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001011000=>8
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001011010=>8
001011011=>6
001011100=>8
001011101=>7
001011110=>7
001011111=>6
001100000=>7
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001110111=>7
001111000=>8
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001111111=>7
010000000=>8
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010001000=>7
010001001=>7
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010001011=>7
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010001101=>7
010001110=>7
010001111=>5
010010000=>7
010010001=>7
010010010=>9
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010010100=>7
010010101=>7
010010110=>7
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010011001=>8
010011010=>8
010011011=>6
010011100=>7
010011101=>7
010011110=>7
010011111=>6
010100000=>7
010100001=>7
010100010=>8
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010100110=>8
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010110001=>6
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010110110=>8
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010111110=>8
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011110101=>7
011110110=>8
011110111=>7
011111000=>7
011111001=>7
011111010=>8
011111011=>7
011111100=>8
011111101=>8
011111110=>9
011111111=>8
100000000=>8
100000001=>9
100000010=>8
100000011=>8
100000100=>7
100000101=>8
100000110=>7
100000111=>7
100001000=>7
100001001=>8
100001010=>7
100001011=>7
100001100=>6
100001101=>7
100001110=>6
100001111=>6
100010000=>7
100010001=>9
100010010=>7
100010011=>7
100010100=>7
100010101=>7
100010110=>6
100010111=>6
100011000=>8
100011001=>8
100011010=>6
100011011=>6
100011100=>7
100011101=>7
100011110=>6
100011111=>6
100100000=>7
100100001=>8
100100010=>7
100100011=>7
100100100=>8
100100101=>8
100100110=>7
100100111=>7
100101000=>7
100101001=>9
100101010=>7
100101011=>7
100101100=>7
100101101=>7
100101110=>6
100101111=>6
100110000=>6
100110001=>8
100110010=>8
100110011=>8
100110100=>7
100110101=>8
100110110=>7
100110111=>7
100111000=>7
100111001=>9
100111010=>7
100111011=>7
100111100=>8
100111101=>8
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101000000=>7
101000001=>8
101000010=>8
101000011=>8
101000100=>7
101000101=>9
101000110=>7
101000111=>7
101001000=>7
101001001=>8
101001010=>8
101001011=>8
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101001101=>8
101001110=>6
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101011101=>8
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101111111=>8
110000000=>7
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110000111=>8
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110001111=>7
110010000=>6
110010001=>7
110010010=>7
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110010100=>7
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110011000=>6
110011001=>8
110011010=>6
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110011100=>7
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110011110=>6
110011111=>7
110100000=>6
110100001=>7
110100010=>7
110100011=>8
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110100101=>8
110100110=>7
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110101000=>5
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110101010=>7
110101011=>9
110101100=>7
110101101=>7
110101110=>7
110101111=>7
110110000=>5
110110001=>6
110110010=>6
110110011=>8
110110100=>6
110110101=>8
110110110=>8
110110111=>8
110111000=>5
110111001=>7
110111010=>7
110111011=>9
110111100=>6
110111101=>8
110111110=>7
110111111=>8
111000000=>6
111000001=>7
111000010=>6
111000011=>8
111000100=>5
111000101=>7
111000110=>7
111000111=>9
111001000=>5
111001001=>7
111001010=>6
111001011=>8
111001100=>6
111001101=>8
111001110=>8
111001111=>8
111010000=>5
111010001=>6
111010010=>6
111010011=>7
111010100=>5
111010101=>7
111010110=>7
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111011000=>5
111011001=>7
111011010=>7
111011011=>8
111011100=>7
111011101=>7
111011110=>7
111011111=>8
111100000=>5
111100001=>6
111100010=>5
111100011=>7
111100100=>5
111100101=>6
111100110=>6
111100111=>8
111101000=>5
111101001=>6
111101010=>6
111101011=>7
111101100=>6
111101101=>7
111101110=>7
111101111=>9
111110000=>5
111110001=>6
111110010=>6
111110011=>7
111110100=>6
111110101=>7
111110110=>7
111110111=>8
111111000=>6
111111001=>7
111111010=>7
111111011=>8
111111100=>7
111111101=>8
111111110=>8
111111111=>9
                    

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Description

The length of a longest palindromic subword of a binary word.
A subword of a word is a word obtained by deleting letters. This statistic records the maximal length of a palindromic subword.
Any binary word of length $n$ contains a palindromic subword of length at least $n/2$, obtained by removing all occurrences of the letter which occurs less often. This bound is obtained by the word beginning with $n/2$ zeros and ending with $n/2$ ones.

Code

def statistic(w):
    for k in range(len(w), Integer(0), -Integer(1)):
        for s in Subwords(w, k):
            if s == s[::-Integer(1)]:
                return k

Created

Jun 11, 2019 at 11:28 by Martin Rubey

Updated

Jun 11, 2019 at 11:28 by Martin Rubey