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Identifier
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 [2,1,3,1]=>2 [2,1,4]=>2 [2,2,1,1,1]=>2 [2,2,1,2]=>2 [2,2,2,1]=>2 [2,2,3]=>3 [2,3,1,1]=>2 [2,3,2]=>2 [2,4,1]=>2 [2,5]=>2 [3,1,1,1,1]=>1 [3,1,1,2]=>2 [3,1,2,1]=>2 [3,1,3]=>2 [3,2,1,1]=>2 [3,2,2]=>2 [3,3,1]=>2 [3,4]=>2 [4,1,1,1]=>1 [4,1,2]=>2 [4,2,1]=>2 [4,3]=>2 [5,1,1]=>1 [5,2]=>2 [6,1]=>1 [7]=>1 [1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,2]=>2 [1,1,1,1,1,2,1]=>2 [1,1,1,1,1,3]=>2 [1,1,1,1,2,1,1]=>2 [1,1,1,1,2,2]=>2 [1,1,1,1,3,1]=>2 [1,1,1,1,4]=>2 [1,1,1,2,1,1,1]=>2 [1,1,1,2,1,2]=>2 [1,1,1,2,2,1]=>2 [1,1,1,2,3]=>3 [1,1,1,3,1,1]=>2 [1,1,1,3,2]=>2 [1,1,1,4,1]=>2 [1,1,1,5]=>2 [1,1,2,1,1,1,1]=>2 [1,1,2,1,1,2]=>2 [1,1,2,1,2,1]=>2 [1,1,2,1,3]=>3 [1,1,2,2,1,1]=>2 [1,1,2,2,2]=>2 [1,1,2,3,1]=>3 [1,1,2,4]=>3 [1,1,3,1,1,1]=>2 [1,1,3,1,2]=>2 [1,1,3,2,1]=>2 [1,1,3,3]=>3 [1,1,4,1,1]=>2 [1,1,4,2]=>2 [1,1,5,1]=>2 [1,1,6]=>2 [1,2,1,1,1,1,1]=>2 [1,2,1,1,1,2]=>2 [1,2,1,1,2,1]=>2 [1,2,1,1,3]=>3 [1,2,1,2,1,1]=>2 [1,2,1,2,2]=>2 [1,2,1,3,1]=>3 [1,2,1,4]=>3 [1,2,2,1,1,1]=>2 [1,2,2,1,2]=>2 [1,2,2,2,1]=>2 [1,2,2,3]=>3 [1,2,3,1,1]=>3 [1,2,3,2]=>3 [1,2,4,1]=>3 [1,2,5]=>3 [1,3,1,1,1,1]=>2 [1,3,1,1,2]=>2 [1,3,1,2,1]=>2 [1,3,1,3]=>3 [1,3,2,1,1]=>2 [1,3,2,2]=>2 [1,3,3,1]=>3 [1,3,4]=>3 [1,4,1,1,1]=>2 [1,4,1,2]=>2 [1,4,2,1]=>2 [1,4,3]=>3 [1,5,1,1]=>2 [1,5,2]=>2 [1,6,1]=>2 [1,7]=>2 [2,1,1,1,1,1,1]=>1 [2,1,1,1,1,2]=>2 [2,1,1,1,2,1]=>2 [2,1,1,1,3]=>2 [2,1,1,2,1,1]=>2 [2,1,1,2,2]=>2 [2,1,1,3,1]=>2 [2,1,1,4]=>2 [2,1,2,1,1,1]=>2 [2,1,2,1,2]=>2 [2,1,2,2,1]=>2 [2,1,2,3]=>3 [2,1,3,1,1]=>2 [2,1,3,2]=>2 [2,1,4,1]=>2 [2,1,5]=>2 [2,2,1,1,1,1]=>2 [2,2,1,1,2]=>2 [2,2,1,2,1]=>2 [2,2,1,3]=>3 [2,2,2,1,1]=>2 [2,2,2,2]=>2 [2,2,3,1]=>3 [2,2,4]=>3 [2,3,1,1,1]=>2 [2,3,1,2]=>2 [2,3,2,1]=>2 [2,3,3]=>3 [2,4,1,1]=>2 [2,4,2]=>2 [2,5,1]=>2 [2,6]=>2 [3,1,1,1,1,1]=>1 [3,1,1,1,2]=>2 [3,1,1,2,1]=>2 [3,1,1,3]=>2 [3,1,2,1,1]=>2 [3,1,2,2]=>2 [3,1,3,1]=>2 [3,1,4]=>2 [3,2,1,1,1]=>2 [3,2,1,2]=>2 [3,2,2,1]=>2 [3,2,3]=>3 [3,3,1,1]=>2 [3,3,2]=>2 [3,4,1]=>2 [3,5]=>2 [4,1,1,1,1]=>1 [4,1,1,2]=>2 [4,1,2,1]=>2 [4,1,3]=>2 [4,2,1,1]=>2 [4,2,2]=>2 [4,3,1]=>2 [4,4]=>2 [5,1,1,1]=>1 [5,1,2]=>2 [5,2,1]=>2 [5,3]=>2 [6,1,1]=>1 [6,2]=>2 [7,1]=>1 [8]=>1 [1,1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,1,2]=>2 [1,1,1,1,1,1,2,1]=>2 [1,1,1,1,1,1,3]=>2 [1,1,1,1,1,2,1,1]=>2 [1,1,1,1,1,2,2]=>2 [1,1,1,1,1,3,1]=>2 [1,1,1,1,1,4]=>2 [1,1,1,1,2,1,1,1]=>2 [1,1,1,1,2,1,2]=>2 [1,1,1,1,2,2,1]=>2 [1,1,1,1,2,3]=>3 [1,1,1,1,3,1,1]=>2 [1,1,1,1,3,2]=>2 [1,1,1,1,4,1]=>2 [1,1,1,1,5]=>2 [1,1,1,2,1,1,1,1]=>2 [1,1,1,2,1,1,2]=>2 [1,1,1,2,1,2,1]=>2 [1,1,1,2,1,3]=>3 [1,1,1,2,2,1,1]=>2 [1,1,1,2,2,2]=>2 [1,1,1,2,3,1]=>3 [1,1,1,2,4]=>3 [1,1,1,3,1,1,1]=>2 [1,1,1,3,1,2]=>2 [1,1,1,3,2,1]=>2 [1,1,1,3,3]=>3 [1,1,1,4,1,1]=>2 [1,1,1,4,2]=>2 [1,1,1,5,1]=>2 [1,1,1,6]=>2 [1,1,2,1,1,1,1,1]=>2 [1,1,2,1,1,1,2]=>2 [1,1,2,1,1,2,1]=>2 [1,1,2,1,1,3]=>3 [1,1,2,1,2,1,1]=>2 [1,1,2,1,2,2]=>2 [1,1,2,1,3,1]=>3 [1,1,2,1,4]=>3 [1,1,2,2,1,1,1]=>2 [1,1,2,2,1,2]=>2 [1,1,2,2,2,1]=>2 [1,1,2,2,3]=>3 [1,1,2,3,1,1]=>3 [1,1,2,3,2]=>3 [1,1,2,4,1]=>3 [1,1,2,5]=>3 [1,1,3,1,1,1,1]=>2 [1,1,3,1,1,2]=>2 [1,1,3,1,2,1]=>2 [1,1,3,1,3]=>3 [1,1,3,2,1,1]=>2 [1,1,3,2,2]=>2 [1,1,3,3,1]=>3 [1,1,3,4]=>3 [1,1,4,1,1,1]=>2 [1,1,4,1,2]=>2 [1,1,4,2,1]=>2 [1,1,4,3]=>3 [1,1,5,1,1]=>2 [1,1,5,2]=>2 [1,1,6,1]=>2 [1,1,7]=>2 [1,2,1,1,1,1,1,1]=>2 [1,2,1,1,1,1,2]=>2 [1,2,1,1,1,2,1]=>2 [1,2,1,1,1,3]=>3 [1,2,1,1,2,1,1]=>2 [1,2,1,1,2,2]=>2 [1,2,1,1,3,1]=>3 [1,2,1,1,4]=>3 [1,2,1,2,1,1,1]=>2 [1,2,1,2,1,2]=>2 [1,2,1,2,2,1]=>2 [1,2,1,2,3]=>3 [1,2,1,3,1,1]=>3 [1,2,1,3,2]=>3 [1,2,1,4,1]=>3 [1,2,1,5]=>3 [1,2,2,1,1,1,1]=>2 [1,2,2,1,1,2]=>2 [1,2,2,1,2,1]=>2 [1,2,2,1,3]=>3 [1,2,2,2,1,1]=>2 [1,2,2,2,2]=>2 [1,2,2,3,1]=>3 [1,2,2,4]=>3 [1,2,3,1,1,1]=>3 [1,2,3,1,2]=>3 [1,2,3,2,1]=>3 [1,2,3,3]=>3 [1,2,4,1,1]=>3 [1,2,4,2]=>3 [1,2,5,1]=>3 [1,2,6]=>3 [1,3,1,1,1,1,1]=>2 [1,3,1,1,1,2]=>2 [1,3,1,1,2,1]=>2 [1,3,1,1,3]=>3 [1,3,1,2,1,1]=>2 [1,3,1,2,2]=>2 [1,3,1,3,1]=>3 [1,3,1,4]=>3 [1,3,2,1,1,1]=>2 [1,3,2,1,2]=>2 [1,3,2,2,1]=>2 [1,3,2,3]=>3 [1,3,3,1,1]=>3 [1,3,3,2]=>3 [1,3,4,1]=>3 [1,3,5]=>3 [1,4,1,1,1,1]=>2 [1,4,1,1,2]=>2 [1,4,1,2,1]=>2 [1,4,1,3]=>3 [1,4,2,1,1]=>2 [1,4,2,2]=>2 [1,4,3,1]=>3 [1,4,4]=>3 [1,5,1,1,1]=>2 [1,5,1,2]=>2 [1,5,2,1]=>2 [1,5,3]=>3 [1,6,1,1]=>2 [1,6,2]=>2 [1,7,1]=>2 [1,8]=>2 [2,1,1,1,1,1,1,1]=>1 [2,1,1,1,1,1,2]=>2 [2,1,1,1,1,2,1]=>2 [2,1,1,1,1,3]=>2 [2,1,1,1,2,1,1]=>2 [2,1,1,1,2,2]=>2 [2,1,1,1,3,1]=>2 [2,1,1,1,4]=>2 [2,1,1,2,1,1,1]=>2 [2,1,1,2,1,2]=>2 [2,1,1,2,2,1]=>2 [2,1,1,2,3]=>3 [2,1,1,3,1,1]=>2 [2,1,1,3,2]=>2 [2,1,1,4,1]=>2 [2,1,1,5]=>2 [2,1,2,1,1,1,1]=>2 [2,1,2,1,1,2]=>2 [2,1,2,1,2,1]=>2 [2,1,2,1,3]=>3 [2,1,2,2,1,1]=>2 [2,1,2,2,2]=>2 [2,1,2,3,1]=>3 [2,1,2,4]=>3 [2,1,3,1,1,1]=>2 [2,1,3,1,2]=>2 [2,1,3,2,1]=>2 [2,1,3,3]=>3 [2,1,4,1,1]=>2 [2,1,4,2]=>2 [2,1,5,1]=>2 [2,1,6]=>2 [2,2,1,1,1,1,1]=>2 [2,2,1,1,1,2]=>2 [2,2,1,1,2,1]=>2 [2,2,1,1,3]=>3 [2,2,1,2,1,1]=>2 [2,2,1,2,2]=>2 [2,2,1,3,1]=>3 [2,2,1,4]=>3 [2,2,2,1,1,1]=>2 [2,2,2,1,2]=>2 [2,2,2,2,1]=>2 [2,2,2,3]=>3 [2,2,3,1,1]=>3 [2,2,3,2]=>3 [2,2,4,1]=>3 [2,2,5]=>3 [2,3,1,1,1,1]=>2 [2,3,1,1,2]=>2 [2,3,1,2,1]=>2 [2,3,1,3]=>3 [2,3,2,1,1]=>2 [2,3,2,2]=>2 [2,3,3,1]=>3 [2,3,4]=>3 [2,4,1,1,1]=>2 [2,4,1,2]=>2 [2,4,2,1]=>2 [2,4,3]=>3 [2,5,1,1]=>2 [2,5,2]=>2 [2,6,1]=>2 [2,7]=>2 [3,1,1,1,1,1,1]=>1 [3,1,1,1,1,2]=>2 [3,1,1,1,2,1]=>2 [3,1,1,1,3]=>2 [3,1,1,2,1,1]=>2 [3,1,1,2,2]=>2 [3,1,1,3,1]=>2 [3,1,1,4]=>2 [3,1,2,1,1,1]=>2 [3,1,2,1,2]=>2 [3,1,2,2,1]=>2 [3,1,2,3]=>3 [3,1,3,1,1]=>2 [3,1,3,2]=>2 [3,1,4,1]=>2 [3,1,5]=>2 [3,2,1,1,1,1]=>2 [3,2,1,1,2]=>2 [3,2,1,2,1]=>2 [3,2,1,3]=>3 [3,2,2,1,1]=>2 [3,2,2,2]=>2 [3,2,3,1]=>3 [3,2,4]=>3 [3,3,1,1,1]=>2 [3,3,1,2]=>2 [3,3,2,1]=>2 [3,3,3]=>3 [3,4,1,1]=>2 [3,4,2]=>2 [3,5,1]=>2 [3,6]=>2 [4,1,1,1,1,1]=>1 [4,1,1,1,2]=>2 [4,1,1,2,1]=>2 [4,1,1,3]=>2 [4,1,2,1,1]=>2 [4,1,2,2]=>2 [4,1,3,1]=>2 [4,1,4]=>2 [4,2,1,1,1]=>2 [4,2,1,2]=>2 [4,2,2,1]=>2 [4,2,3]=>3 [4,3,1,1]=>2 [4,3,2]=>2 [4,4,1]=>2 [4,5]=>2 [5,1,1,1,1]=>1 [5,1,1,2]=>2 [5,1,2,1]=>2 [5,1,3]=>2 [5,2,1,1]=>2 [5,2,2]=>2 [5,3,1]=>2 [5,4]=>2 [6,1,1,1]=>1 [6,1,2]=>2 [6,2,1]=>2 [6,3]=>2 [7,1,1]=>1 [7,2]=>2 [8,1]=>1 [9]=>1
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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