GlobalAscents on Permutation
Positions i < n with p(j) < p(k) whenever j <= i < k.
Read through the pigeonhole principle: the largest of the first i entries is at most i.
Called as CombinatorialStat(x, "GlobalAscents"). The head's page has its examples.
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FindStat St000234
The number of global ascents of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 1 |
[2,1] | 0 |
[1,2,3] | 2 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 0 |
[3,1,2] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000234 has the rest.