- FindStat

Identifier

St000922: Binary words ⟶ ℤ

Values

0 => 1

1 => 1

00 => 2

01 => 1

10 => 1

11 => 2

000 => 3

001 => 2

010 => 2

011 => 2

100 => 2

101 => 2

110 => 2

111 => 3

0000 => 4

0001 => 3

0010 => 2

0011 => 2

0100 => 2

0101 => 3

0110 => 2

0111 => 3

1000 => 3

1001 => 2

1010 => 3

1011 => 2

1100 => 2

1101 => 2

1110 => 3

1111 => 4

00000 => 5

00001 => 4

00010 => 3

00011 => 3

00100 => 3

00101 => 3

00110 => 2

00111 => 3

01000 => 3

01001 => 3

01010 => 4

01011 => 3

01100 => 2

01101 => 3

01110 => 3

01111 => 4

10000 => 4

10001 => 3

10010 => 3

10011 => 2

10100 => 3

10101 => 4

10110 => 3

10111 => 3

11000 => 3

11001 => 2

11010 => 3

11011 => 3

11100 => 3

11101 => 3

11110 => 4

11111 => 5

000000 => 6

000001 => 5

000010 => 4

000011 => 4

000100 => 3

000101 => 3

000110 => 3

000111 => 3

001000 => 3

001001 => 4

001010 => 4

001011 => 3

001100 => 3

001101 => 3

001110 => 3

001111 => 4

010000 => 4

010001 => 3

010010 => 4

010011 => 3

010100 => 4

010101 => 5

010110 => 3

010111 => 3

011000 => 3

011001 => 3

011010 => 3

011011 => 4

011100 => 3

011101 => 3

011110 => 4

011111 => 5

100000 => 5

100001 => 4

100010 => 3

100011 => 3

100100 => 4

100101 => 3

100110 => 3

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Description

The minimal number such that all substrings of this length are unique.

References

[1] Aumayr, W. String with all unique substrings MathOverflow:277790

Code

def statistic(w):
    for k in range(1,len(w)+1):
        S = []
        for i in range(len(w)-k+1):
            s = w[i:i+k]
            if s in S:
                break
            else:
                S.append(s)
        else:
            return k

Created

Aug 02, 2017 at 17:04 by Martin Rubey

Updated

Aug 02, 2017 at 17:04 by Martin Rubey