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Identifier

St000293: Binary words ⟶ ℤ

Values

0 => 0

1 => 0

00 => 0

01 => 0

10 => 1

11 => 0

000 => 0

001 => 0

010 => 1

011 => 0

100 => 2

101 => 1

110 => 2

111 => 0

0000 => 0

0001 => 0

0010 => 1

0011 => 0

0100 => 2

0101 => 1

0110 => 2

0111 => 0

1000 => 3

1001 => 2

1010 => 3

1011 => 1

1100 => 4

1101 => 2

1110 => 3

1111 => 0

00000 => 0

00001 => 0

00010 => 1

00011 => 0

00100 => 2

00101 => 1

00110 => 2

00111 => 0

01000 => 3

01001 => 2

01010 => 3

01011 => 1

01100 => 4

01101 => 2

01110 => 3

01111 => 0

10000 => 4

10001 => 3

10010 => 4

10011 => 2

10100 => 5

10101 => 3

10110 => 4

10111 => 1

11000 => 6

11001 => 4

11010 => 5

11011 => 2

11100 => 6

11101 => 3

11110 => 4

11111 => 0

000000 => 0

000001 => 0

000010 => 1

000011 => 0

000100 => 2

000101 => 1

000110 => 2

000111 => 0

001000 => 3

001001 => 2

001010 => 3

001011 => 1

001100 => 4

001101 => 2

001110 => 3

001111 => 0

010000 => 4

010001 => 3

010010 => 4

010011 => 2

010100 => 5

010101 => 3

010110 => 4

010111 => 1

011000 => 6

011001 => 4

011010 => 5

011011 => 2

011100 => 6

011101 => 3

011110 => 4

011111 => 0

100000 => 5

100001 => 4

100010 => 5

100011 => 3

100100 => 6

100101 => 4

100110 => 5

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Description

The number of inversions of a binary word.

Code

def statistic(x):
    return len(x.inversions())

Created

Nov 19, 2015 at 12:14 by Martin Rubey

Updated

Feb 12, 2018 at 22:30 by Martin Rubey