NonEmptyPowerSet - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.
Our website is currently undergoing maintenance, which may result in occasional errors while browsing. We apologize for any inconvenience this may cause and are working swiftly to restore full functionality. Thank you for your patience.

Online Help

All Products    Maple    MapleSim


Hypergraphs[ExampleHypergraphs]

  

NonEmptyPowerSet

  

Return the power set of given order

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

NonEmptyPowerSet(S)

Parameters

S

-

set

Description

• 

The command NonEmptyPowerSet(S) returns the hypergraph with the set S as vertex set and  with all non-empty subsets of S as hyperedges.

Examples

withHypergraphs:withExampleHypergraphs:

Consider the following power set hypergraph.

P4NonEmptyPowerSet1,2,3,4

P4< a hypergraph on 4 vertices with 15 hyperedges >

(1)

Draw a graphical representation of this hypergraph.

DrawP4

Compute its minimal hyperedges.

MMinP4&semi;VerticesM&semi;HyperedgesM

M< a hypergraph on 4 vertices with 4 hyperedges >

1&comma;2&comma;3&comma;4

1&comma;2&comma;3&comma;4

(2)

Compute its maximal hyperedges.

MMaxP4&semi;VerticesM&semi;HyperedgesM

M< a hypergraph on 4 vertices with 1 hyperedges >

1&comma;2&comma;3&comma;4

1&comma;2&comma;3&comma;4

(3)

Consider this other power set hypergraph.

P8NonEmptyPowerSet1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8

P8< a hypergraph on 8 vertices with 255 hyperedges >

(4)

Draw a graphical representation of this hypergraph.

DrawP8

Compute its minimal hyperedges.

MMinP8&semi;VerticesM&semi;HyperedgesM

M< a hypergraph on 8 vertices with 8 hyperedges >

1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8

1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8

(5)

Compute its maximal hyperedges.

MMaxP8&semi;VerticesM&semi;HyperedgesM

M< a hypergraph on 8 vertices with 1 hyperedges >

1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8

1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8

(6)

References

  

Claude Berge. Hypergraphes. Combinatoires des ensembles finis. 1987,  Paris, Gauthier-Villars, translated to English.

  

Claude Berge. Hypergraphs. Combinatorics of Finite Sets.  1989, Amsterdam, North-Holland Mathematical Library, Elsevier, translated from French.

  

Charles Leiserson, Liyun Li, Marc Moreno Maza and Yuzhen Xie " Parallel computation of the minimal elements of a poset." Proceedings of the 4th International Workshop on Parallel Symbolic Computation (PASCO) 2010: 53-62, ACM.

Compatibility

• 

The Hypergraphs[ExampleHypergraphs][NonEmptyPowerSet] command was introduced in Maple 2024.

• 

For more information on Maple 2024 changes, see Updates in Maple 2024.

See Also

Hypergraphs[Max]

Hypergraphs[Min]