Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
Scheduling
Data analysis Topological sorting |
| gptkbp:complexity |
Counting the number of linear extensions is #P-complete.
|
| gptkbp:defines |
A linear extension of a partially ordered set is a total order that is consistent with the partial order.
|
| gptkbp:field |
gptkb:Order_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Linear Extension
|
| gptkbp:property |
Every finite partially ordered set has at least one linear extension (by Szpilrajn's theorem).
|
| gptkbp:relatedTo |
Poset
Partial order Total order Order extension principle |
| gptkbp:supportsAlgorithm |
gptkb:Topological_sort
|
| gptkbp:theory |
gptkb:Szpilrajn_extension_theorem
|
| gptkbp:usedIn |
gptkb:Mathematics
Computer science Combinatorics |
| gptkbp:bfsParent |
gptkb:Topological_Sort
|
| gptkbp:bfsLayer |
7
|