Function Repository Resource:

SetPartitionRefinement

Refine a partition of a set

Contributed by: Jack Heimrath, Wolfram|Alpha Math Team

ResourceFunction["SetPartitionRefinement"][part,piv]

returns the refinement of the partition part by the pivot piv.

ResourceFunction["SetPartitionRefinement"][part,{piv₁,piv₂,…}]

returns the refinement of the partition part by the pivots piv_i.

Details

The argument part must be a List of lists (i.e. it should be a partition of a set).

Refine a given partition of a set:

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Use more than one pivot:

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Create the refined partition of a set based on a collection of partitions:

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The first argument must be a collection of sets, not a set:

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The first argument need not be a valid partition:

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If a collection of sets contains elements with non-trivial intersection, using those particular elements as pivots will return an actual partition:

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To view the full source code for SetPartitionRefinement, evaluate the following: