Recently I found an interesting problem: enumeration of possible antimatroids over finite set.

From combinatorial point of view, an **antimatroid** is a family of sets, with special properties.

Following the wikipedia definition, is an antimatroid iff:

- is
*closed under unions*, that is: - is a
*nonempty**accesible*:

For example, following family is an antimatroid:

From now, I will denote the largest set, being also a superset of every other one in the family, as (so in previous example, ).

Just as matroids are generalization of antichains, antimatroids are generalization of chains.

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