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
|
The object randomPoset is a method function with options.