antichains -- computes all antichains of a poset

Synopsis

Usage:

L = antichains P
Inputs:
- P, an instance of the type Poset,
- k, an integer, if specified length of returned antichains
Outputs:
- L, a list, containing all antichains of $P$

Description

A set of elements of $P$ is called an antichain if no two distinct elements of the set are comparable.

i1 : D = divisorPoset 12;

i2 : antichains D

o2 = {{}, {1}, {2}, {2, 3}, {3}, {3, 4}, {4}, {4, 6}, {6}, {12}}

o2 : List

With the input k, the method restricts to only antichains of that length. In a divisorPoset, all chains of length $2$ describe exactly the non-divisor-multiple pairs.

i3 : antichains(D, 2)

o3 = {{2, 3}, {3, 4}, {4, 6}}

o3 : List

Since every distinct pair of vertices in a chain is comparable, the only antichains of a chain are the singleton sets and the empty set.

i4 : antichains chain 5

o4 = {{}, {1}, {2}, {3}, {4}, {5}}

o4 : List

Ways to use antichains :

antichains(Poset)
antichains(Poset,ZZ)

For the programmer

The object antichains is a method function.

antichains -- computes all antichains of a poset

Synopsis

Description

See also

Ways to use antichains :

For the programmer