Independence system
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In combinatorial mathematics, an independence system is a pair (V, \mathcal{I}) , where is a finite set and is a collection of subsets of (called the independent sets or feasible sets) with the following properties: # The empty set is independent, i.e., \emptyset\in\mathcal{I} . (Alternatively, at least one subset of is independent, i.e., \mathcal{I}\neq\emptyset .) # Every subset of an independent set is independent, i.e., for each Y\subseteq X , we have X\in\mathcal{I}\Rightarrow Y\in\mathcal{I} . This is sometimes called the hereditary property, or downward-closedness. Another term for an independence system is an abstract simplicial complex.
In combinatorial mathematics, an independence system is a pair (V, \mathcal{I}) , where is a finite set and is a collection of subsets of (called the independent sets or feasible sets) with the following properties: The empty set is independent, i.e., \emptyset\in\mathcal{I} . (Alternatively, at least one subset of is independent, i.e., \mathcal{I}\neq\emptyset .) Every subset of an independent set is independent, i.e., for each Y\subseteq X , we have X\in\mathcal{I}\Rightarrow Y\in\mathcal{I} . This is sometimes called the hereditary property, or downward-closedness. Another term for an independence system is an abstract simplicial complex.
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