DecompositionNumber on Permutation
The k with {p(1), ..., p(k)} = {1, ..., k}: the blocks of p as a direct sum.
One more than GlobalAscents; also called the block number.
Called as CombinatorialStat(x, "DecompositionNumber"). The head's page has its examples.
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FindStat St000056
The decomposition (or block) number of a permutation.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 2 |
[2,1] | 1 |
[1,2,3] | 3 |
[1,3,2] | 2 |
[2,1,3] | 2 |
[2,3,1] | 1 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000056 has the rest.