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Independence system ：ウィキペディア英語版

Independence system
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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抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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