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Identifier

St000820: Integer compositions ⟶ ℤ

Values

[1] => 1

[1,1] => 1

[2] => 1

[1,1,1] => 1

[1,2] => 2

[2,1] => 2

[3] => 1

[1,1,1,1] => 1

[1,1,2] => 3

[1,2,1] => 3

[1,3] => 2

[2,1,1] => 3

[2,2] => 1

[3,1] => 2

[4] => 1

[1,1,1,1,1] => 1

[1,1,1,2] => 4

[1,1,2,1] => 4

[1,1,3] => 3

[1,2,1,1] => 4

[1,2,2] => 3

[1,3,1] => 3

[1,4] => 2

[2,1,1,1] => 4

[2,1,2] => 3

[2,2,1] => 3

[2,3] => 2

[3,1,1] => 3

[3,2] => 2

[4,1] => 2

[5] => 1

[1,1,1,1,1,1] => 1

[1,1,1,1,2] => 5

[1,1,1,2,1] => 5

[1,1,1,3] => 4

[1,1,2,1,1] => 5

[1,1,2,2] => 4

[1,1,3,1] => 4

[1,1,4] => 3

[1,2,1,1,1] => 5

[1,2,1,2] => 2

[1,2,2,1] => 4

[1,2,3] => 3

[1,3,1,1] => 4

[1,3,2] => 3

[1,4,1] => 3

[1,5] => 2

[2,1,1,1,1] => 5

[2,1,1,2] => 4

[2,1,2,1] => 2

[2,1,3] => 3

[2,2,1,1] => 4

[2,2,2] => 1

[2,3,1] => 3

[2,4] => 2

[3,1,1,1] => 4

[3,1,2] => 3

[3,2,1] => 3

[3,3] => 1

[4,1,1] => 3

[4,2] => 2

[5,1] => 2

[6] => 1

[1,1,1,1,1,1,1] => 1

[1,1,1,1,1,2] => 6

[1,1,1,1,2,1] => 6

[1,1,1,1,3] => 5

[1,1,1,2,1,1] => 6

[1,1,1,2,2] => 5

[1,1,1,3,1] => 5

[1,1,1,4] => 4

[1,1,2,1,1,1] => 6

[1,1,2,1,2] => 5

[1,1,2,2,1] => 5

[1,1,2,3] => 4

[1,1,3,1,1] => 5

[1,1,3,2] => 4

[1,1,4,1] => 4

[1,1,5] => 3

[1,2,1,1,1,1] => 6

[1,2,1,1,2] => 5

[1,2,1,2,1] => 5

[1,2,1,3] => 4

[1,2,2,1,1] => 5

[1,2,2,2] => 4

[1,2,3,1] => 4

[1,2,4] => 3

[1,3,1,1,1] => 5

[1,3,1,2] => 4

[1,3,2,1] => 4

[1,3,3] => 3

[1,4,1,1] => 4

[1,4,2] => 3

[1,5,1] => 3

[1,6] => 2

[2,1,1,1,1,1] => 6

[2,1,1,1,2] => 5

[2,1,1,2,1] => 5

[2,1,1,3] => 4

[2,1,2,1,1] => 5

[2,1,2,2] => 4

>>> Load all 511 entries. <<<

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Description

The number of compositions obtained by rotating the composition.

Code

def statistic(c):
    rc = c[1:] + [c[0]]
    r = 1
    while rc != c:
        rc = rc[1:] + [rc[0]]
        r += 1
    return r

Created

May 21, 2017 at 22:53 by Martin Rubey

Updated

Nov 19, 2017 at 22:02 by Christian Stump