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, ).