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Identifier

St001524: Binary words ⟶ ℤ

Values

0 => 0

1 => 0

00 => 1

01 => 0

10 => 0

11 => 1

000 => 1

001 => 0

010 => 1

011 => 0

100 => 0

101 => 1

110 => 0

111 => 1

0000 => 2

0001 => 1

0010 => 1

0011 => 0

0100 => 1

0101 => 0

0110 => 2

0111 => 1

1000 => 1

1001 => 2

1010 => 0

1011 => 1

1100 => 0

1101 => 1

1110 => 1

1111 => 2

00000 => 2

00001 => 1

00010 => 1

00011 => 0

00100 => 2

00101 => 1

00110 => 1

00111 => 0

01000 => 1

01001 => 0

01010 => 2

01011 => 1

01100 => 1

01101 => 0

01110 => 2

01111 => 1

10000 => 1

10001 => 2

10010 => 0

10011 => 1

10100 => 1

10101 => 2

10110 => 0

10111 => 1

11000 => 0

11001 => 1

11010 => 1

11011 => 2

11100 => 0

11101 => 1

11110 => 1

11111 => 2

000000 => 3

000001 => 2

000010 => 2

000011 => 1

000100 => 2

000101 => 1

000110 => 1

000111 => 0

001000 => 2

001001 => 1

001010 => 1

001011 => 0

001100 => 3

001101 => 2

001110 => 2

001111 => 1

010000 => 2

010001 => 1

010010 => 3

010011 => 2

010100 => 1

010101 => 0

010110 => 2

010111 => 1

011000 => 1

011001 => 0

011010 => 2

011011 => 1

011100 => 2

011101 => 1

011110 => 3

011111 => 2

100000 => 2

100001 => 3

100010 => 1

100011 => 2

100100 => 1

100101 => 2

100110 => 0

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Description

The degree of symmetry of a binary word.
For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.

Code

def statistic(D):
    result = sum(1 for a, b in zip(D, D[::-1]) if a == b)
    if is_even(len(D)):
        return result/2
    return (result-1)/2

Created

Mar 02, 2020 at 21:32 by Martin Rubey

Updated

Mar 02, 2020 at 21:32 by Martin Rubey