CycleType from Permutation
The multiset of cycle lengths, as a partition.
The first map here that CROSSES carriers — permutation in, integer partition out — which is the case the types exist for.
Called as CombinatorialMap(x, "CycleType"). The head's page has its examples.
Live
FindStat Mp00108
cycle type
Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.
The cycle type of a permutation as a partition.
| Object | Image |
|---|---|
[1] | [1] |
[1,2] | [1,1] |
[2,1] | [2] |
[1,2,3] | [1,1,1] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00108 has the rest.