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Identifier

St001485: Binary words ⟶ ℤ

Values

0 => 0

1 => 0

00 => 0

01 => 0

10 => 1

11 => 0

000 => 0

001 => 0

010 => 2

011 => 0

100 => 1

101 => 1

110 => 2

111 => 0

0000 => 0

0001 => 0

0010 => 3

0011 => 0

0100 => 2

0101 => 2

0110 => 3

0111 => 0

1000 => 1

1001 => 1

1010 => 0

1011 => 1

1100 => 2

1101 => 2

1110 => 3

1111 => 0

00000 => 0

00001 => 0

00010 => 4

00011 => 0

00100 => 3

00101 => 3

00110 => 4

00111 => 0

01000 => 2

01001 => 2

01010 => 1

01011 => 2

01100 => 3

01101 => 3

01110 => 4

01111 => 0

10000 => 1

10001 => 1

10010 => 0

10011 => 1

10100 => 4

10101 => 4

10110 => 0

10111 => 1

11000 => 2

11001 => 2

11010 => 1

11011 => 2

11100 => 3

11101 => 3

11110 => 4

11111 => 0

000000 => 0

000001 => 0

000010 => 5

000011 => 0

000100 => 4

000101 => 4

000110 => 5

000111 => 0

001000 => 3

001001 => 3

001010 => 2

001011 => 3

001100 => 4

001101 => 4

001110 => 5

001111 => 0

010000 => 2

010001 => 2

010010 => 1

010011 => 2

010100 => 0

010101 => 0

010110 => 1

010111 => 2

011000 => 3

011001 => 3

011010 => 2

011011 => 3

011100 => 4

011101 => 4

011110 => 5

011111 => 0

100000 => 1

100001 => 1

100010 => 0

100011 => 1

100100 => 5

100101 => 5

100110 => 0

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Description

The modular major index of a binary word.
This is St000290The major index of a binary word. modulo the length of the word.

References

[1] Swanson, J. P. Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics MathSciNet:3885578

Code

def statistic(w):
    return w.major_index() % len(w)

Created

Oct 24, 2019 at 13:25 by Martin Rubey

Updated

Oct 24, 2019 at 13:25 by Martin Rubey