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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== *. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「independence system」の詳細全文を読む スポンサード リンク
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