notatio

Surjection ​

The singular-inhabitant constructor for a surjection from positions onto 1..k, as its word.

OEISA000670via SurjectionsA019538via SurjectionsSageMathOrderedSetPartitions(n)via SurjectionsOrderedSetPartitions(n, k)via SurjectionsOntoK
Surjection(list)The singular-inhabitant constructor for a surjection from positions onto 1..k, as its word.
Typed signatures
TypePackageApplies
((list<integer>) -> surjection) & ((set_composition) -> surjection)combinatoricsalways

Domain: Collections

Maps

Into and out of Surjection, called as CombinatorialMap(x, "Name"). Properties are the laws we state and what FindStat records.

From Surjection

  • SetCompositionSurjection → SetCompositioninverseThe set composition a surjection labels: block j holds the positions labelled j.

To Surjection

  • SurjectionSetComposition → SurjectioninverseA set composition as a surjection: each position labelled with its block's index, from 1.

Examples

Basic #

From a set composition: each position labelled with its block, from 1

live ↗
InSurjection⁡(SetComposition⁡([[2,4],[1],[3]]))\operatorname{Surjection}({\operatorname{SetComposition}}([[2, 4], [1], [3]]))OutSurjection⁡([2,1,3,1]){\operatorname{Surjection}}([2, 1, 3, 1])
About
Examples1
CrosswalkOEIS ×2SageMath ×2