BargraphHalfPerimeter on IntegerComposition
Up steps plus horizontal steps of the bargraph.
Deutsch and Elizalde, A bijection between bargraphs and Dyck paths, and FindStat call it the semiperimeter.
Called as CombinatorialStat(x, "BargraphHalfPerimeter"). 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 St000806
The semiperimeter of the associated bargraph.
| Object | Value |
|---|---|
[2] | 3 |
[3] | 4 |
[4] | 5 |
[5] | 6 |
[6] | 7 |
[7] | 8 |
[8] | 9 |
[9] | 10 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000806 has the rest.