SetComposition
The singular-inhabitant constructor for a composition of a set, as its ordered blocks.
Wikipedia
Weak orderingWikidataQ1414271OEISA000670via SetCompositionsSageMathOrderedSetPartitions(n)via SetCompositionsSetComposition(list)The singular-inhabitant constructor for a composition of a set, as its ordered blocks.Typed signatures
| Type | Package | Applies |
|---|---|---|
((list<list<integer>>) -> set_composition) & ((surjection) -> set_composition) | combinatorics | always |
Maps
Into and out of SetComposition, called as CombinatorialMap(x, "Name"). Properties are the laws we state and what FindStat records.
From SetComposition
- BlockConcatenationSetComposition → PermutationsurjectionSurjectionGraded mapMp00286The permutation that lists the blocks in order, each sorted increasingly.
- BlockSizeCompositionSetComposition → IntegerCompositionsurjectionSurjectionGraded mapMp00287The block sizes of a set composition, its blocks taken in order.
- ComplementSetComposition → SetCompositioninvolutionGraded mapInvolutionMp00289Each element i replaced by n + 1 - i, the blocks staying in their order.
- CyclicShiftSetComposition → SetCompositioninverseBijectionGraded mapMp00292The first block moved to the end.
- InverseCyclicShiftSetComposition → SetCompositioninverseBijectionGraded mapMp00291The last block moved to the front.
- ReverseSetComposition → SetCompositioninvolutionGraded mapInvolutionMp00288The blocks in the opposite order.
- SurjectionSetComposition → SurjectioninverseA set composition as a surjection: each position labelled with its block's index, from 1.
- UnderlyingSetPartitionSetComposition → SetPartitionsurjectionSurjectionGraded mapMp00285The set partition with the same blocks, the order of the blocks forgotten.
To SetComposition
- SetCompositionSurjection → SetCompositioninverseThe set composition a surjection labels: block j holds the positions labelled j.
1 more in FindStat, not implemented here
- Mp00290ParkingFunction → SetCompositionSurjectionGraded mapto ordered set partition