notatio

CycleType ​

The multiset of cycle lengths, as a partition.

WikipediaCyclic permutationMathWorldPermutationCycleCyclicPermutationWikidataQ212130nLabcyclic permutationFindStatMp00108via Permutation
CycleType(Permutation)The multiset of cycle lengths, as a partition.
Typed signatures
TypePackageApplies
(permutation) -> integer_partitioncombinatoricsalways

Domain: Combinatorial maps

Details
  • Takes a Permutation and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
  • The first map here that CROSSES carriers — permutation in, integer partition out — which is the case the types exist for.

Examples

Basic #

the one-line word 231231

live ↗
InCycleType(Permutation⁡([2,3,1]))\mathrm{CycleType}({\operatorname{Permutation}}([2, 3, 1]))OutIntegerPartition⁡([3]){\operatorname{IntegerPartition}}([3])
About
Examples1
CrosswalkWikipediaMathWorld ×2WikidatanLabFindStat