Function Repository Resource:

MaximalSubsets

Prune non-maximal subsets from a list of subsets

Contributed by: Carl Woll

ResourceFunction["MaximalSubsets"][list]

prunes non-maximal subsets from the sets in list.

Details and Options

A non-maximal subset is a list which is completely contained in another subset.

The argument list should be a list of subsets, where each subset is a list of elements.

Here is a list of sets:

In[1]:=

Remove the non-maximal subsets {d}, {a}, and {a,b}:

In[2]:=

Out[2]=

MaximalSubsets can handle a large list of subsets:

In[3]:=

The number of maximal subsets:

In[4]:=

Out[4]=

Uses Internal`ListMin, which is based on the BCL algorithm discussed here: https://dl.acm.org/citation.cfm?id=320196.