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Identifier

St000758: Integer compositions ⟶ ℤ

Values

[1] => 1

[1,1] => 1

[2] => 1

[1,1,1] => 1

[1,2] => 2

[2,1] => 1

[3] => 1

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

[1,1,2] => 2

[1,2,1] => 2

[1,3] => 2

[2,1,1] => 1

[2,2] => 2

[3,1] => 1

[4] => 1

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

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

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

[1,1,3] => 2

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

[1,2,2] => 2

[1,3,1] => 2

[1,4] => 2

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

[2,1,2] => 2

[2,2,1] => 2

[2,3] => 2

[3,1,1] => 1

[3,2] => 2

[4,1] => 1

[5] => 1

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

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

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

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

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

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

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

[1,1,4] => 2

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

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

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

[1,2,3] => 3

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

[1,3,2] => 2

[1,4,1] => 2

[1,5] => 2

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

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

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

[2,1,3] => 2

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

[2,2,2] => 2

[2,3,1] => 2

[2,4] => 2

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

[3,1,2] => 2

[3,2,1] => 2

[3,3] => 2

[4,1,1] => 1

[4,2] => 2

[5,1] => 1

[6] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,5] => 2

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

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

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

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

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

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

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

[1,2,4] => 3

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

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

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

[1,3,3] => 3

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

[1,4,2] => 2

[1,5,1] => 2

[1,6] => 2

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

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

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

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

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

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

>>> Load all 511 entries. <<<

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Description

The length of the longest staircase fitting into an integer composition.
For a given composition $c_1,\dots,c_n$, this is the maximal number $\ell$ such that there are indices $i_1 < \dots < i_\ell$ with $c_{i_k} \geq k$, see [def.3.1, 1]

References

[1] Skandera, M. An Eulerian partner for inversions MathSciNet:1848722

Code

def statistic(w):
    l = 0
    for e in w:
        if e > l:
            l += 1
    return l

Created

Apr 09, 2017 at 10:46 by Martin Rubey

Updated

Nov 06, 2017 at 23:33 by Martin Rubey