Independence system
From Infogalactic: the planetary knowledge core
In combinatorial mathematics, an independence system S is a pair (E, I), where E is a finite set and I is a collection of subsets of E (called the independent sets) with the following properties:
- The empty set is independent, i.e., ∅ ∈ I. (Alternatively, at least one subset of E is independent, i.e., I ≠ ∅.)
- Every subset of an independent set is independent, i.e., for each E' ⊆ E, E ∈ I → E' ∈ I. This is sometimes called the hereditary property.
Adding the augmentation property or the independent set exchange property yields a matroid.
For a more general description, see abstract simplicial complex.
References
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