FirstDirectSummandSize on Permutation
The smallest k with {p(1), ..., p(k)} = {1, ..., k}.
Called as CombinatorialStat(x, "FirstDirectSummandSize"). The head's page has its examples.
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FindStat St000501
The size of the first part in the decomposition of a permutation.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 1 |
[2,1] | 2 |
[1,2,3] | 1 |
[1,3,2] | 1 |
[2,1,3] | 2 |
[2,3,1] | 3 |
[3,1,2] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000501 has the rest.