LongestStaircase on IntegerComposition
The greatest l with parts at positions i_1 < ... < i_l such that part i_m is at least m.
Skandera, An Eulerian partner for inversions (Definition 3.1): taking each part that exceeds the staircase so far is optimal.
Called as CombinatorialStat(x, "LongestStaircase"). The head's page has its examples.
Live
Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000758
The length of the longest staircase fitting into an integer composition.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000758 has the rest.