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Identifier

St000900: Integer compositions ⟶ ℤ

Values

[1] => 1

[1,1] => 2

[2] => 1

[1,1,1] => 3

[1,2] => 1

[2,1] => 1

[3] => 1

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

[1,1,2] => 1

[1,2,1] => 1

[1,3] => 1

[2,1,1] => 1

[2,2] => 2

[3,1] => 1

[4] => 1

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

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

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

[1,1,3] => 1

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

[1,2,2] => 1

[1,3,1] => 1

[1,4] => 1

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

[2,1,2] => 1

[2,2,1] => 1

[2,3] => 1

[3,1,1] => 1

[3,2] => 1

[4,1] => 1

[5] => 1

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

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

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

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

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

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

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

[1,1,4] => 1

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

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

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

[1,2,3] => 1

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

[1,3,2] => 1

[1,4,1] => 1

[1,5] => 1

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

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

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

[2,1,3] => 1

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

[2,2,2] => 3

[2,3,1] => 1

[2,4] => 1

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

[3,1,2] => 1

[3,2,1] => 1

[3,3] => 2

[4,1,1] => 1

[4,2] => 1

[5,1] => 1

[6] => 1

[1,1,1,1,1,1,1] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,5] => 1

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

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

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

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

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

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

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

[1,2,4] => 1

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

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

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

[1,3,3] => 1

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

[1,4,2] => 1

[1,5,1] => 1

[1,6] => 1

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

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

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

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

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

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

>>> Load all 511 entries. <<<

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Description

The minimal number of repetitions of a part in an integer composition.
This is the smallest letter in the word obtained by applying the delta morphism.

Code

def statistic(c):
    return min(Word(c).delta())

Created

Jul 17, 2017 at 08:51 by Martin Rubey

Updated

Nov 19, 2017 at 22:02 by Christian Stump