randomPoset -- generates a random poset with a given relation probability

Usage:

P = randomPoset n

P = randomPoset G

P = randomPoset(n, Bias => RR)

P = randomPoset(G, Bias => RR)
Inputs:
- n, an integer, the number of vertices in the poset
- G, a list, the ground set of the poset
Optional inputs:
- Bias => a real number, default value .5, the probability that a given relation will be present
Outputs:
- P, an instance of the type Poset,

Description

This method generates a random poset with a given ground set ($\{1, \ldots, n\}$, if $n$ is specified).

i1 : randomPoset 10

o1 = Relation Matrix: | 1 0 0 1 0 1 1 1 1 1 |
                      | 0 1 0 0 1 1 1 1 1 1 |
                      | 0 0 1 1 0 1 1 1 1 1 |
                      | 0 0 0 1 0 0 0 1 0 0 |
                      | 0 0 0 0 1 1 1 0 1 1 |
                      | 0 0 0 0 0 1 1 0 1 0 |
                      | 0 0 0 0 0 0 1 0 1 0 |
                      | 0 0 0 0 0 0 0 1 0 0 |
                      | 0 0 0 0 0 0 0 0 1 0 |
                      | 0 0 0 0 0 0 0 0 0 1 |

o1 : Poset

The option Bias determines the probability that a given relation will be present. A higher Bias will lead to more relations.

i2 : randomPoset(10, Bias => 0.1)

o2 = Relation Matrix: | 1 0 0 0 1 0 1 1 0 0 |
                      | 0 1 0 0 0 0 0 0 0 0 |
                      | 0 0 1 0 0 0 0 0 0 0 |
                      | 0 0 0 1 1 0 0 0 0 0 |
                      | 0 0 0 0 1 0 0 0 0 0 |
                      | 0 0 0 0 0 1 0 0 0 1 |
                      | 0 0 0 0 0 0 1 1 0 0 |
                      | 0 0 0 0 0 0 0 1 0 0 |
                      | 0 0 0 0 0 0 0 0 1 0 |
                      | 0 0 0 0 0 0 0 0 0 1 |

o2 : Poset

i3 : randomPoset(10, Bias => 0.9)

o3 = Relation Matrix: | 1 1 1 1 1 1 1 1 1 1 |
                      | 0 1 1 1 1 1 1 1 1 1 |
                      | 0 0 1 1 1 1 1 1 1 1 |
                      | 0 0 0 1 1 1 1 1 1 1 |
                      | 0 0 0 0 1 1 1 1 1 1 |
                      | 0 0 0 0 0 1 1 1 1 1 |
                      | 0 0 0 0 0 0 1 1 1 1 |
                      | 0 0 0 0 0 0 0 1 1 1 |
                      | 0 0 0 0 0 0 0 0 1 1 |
                      | 0 0 0 0 0 0 0 0 0 1 |

o3 : Poset

Ways to use randomPoset:

randomPoset(List)
randomPoset(ZZ)

For the programmer

The object randomPoset is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:3824:0.

randomPoset -- generates a random poset with a given relation probability

Description

See also

Ways to use randomPoset:

For the programmer