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Single-Element Unions

This process is used to compute all possible single-element unions of a collection of sets.

Let C denote a collection of sets, and let Ci denote the i-th set in C. Single-element unions are created by sampling a single element from each Ci. Single-element unions are themselves sets, and they contain (at least) one element from each Ci. If all Ci are disjoint, then each single-element union created from C will contain only a single element from each Ci. If some Ci contain elements in common, however, a single-element union may contain multiple elements from a single Ci. Note the difference between single-element unions and strict single-element unions.

For example, the single-element unions of the collection of sets:

{A, B, C},
{C, D},
{E},

are:

{A, C, E},
{A, D, E},
{B, C, E},
{B, D, E},
{C, E},
{C, D, E}.

Here is the set of keywords this process understands, along with a description of their possible corresponding values. See the command line documentation for more information about keyword-value pairs.


Required Keywords Possible Values
Process Single-Element Unions
Set File The name of the file containing a collection of sets. See Set Files for further information.
Output File Name The desired name of the file where the single-element unions will be stored. See Set Files for further information.

Examples

Click here for an example.