独立集合族

【どくりつしゅうごうぞく (independent set family)】

有限集合 $N\,$ とその部分集合族 ${\mathcal {I}}\,$ が以下の (I0)-(I2) を満たすとき, 構文解析に失敗 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\mathbf {M} }=(N,{\mathcal {I}})\,} をマトロイドと呼び, ${\mathcal {I}}\,$ を 構文解析に失敗 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\mathbf {M} }\,} の独立集合族と呼ぶ.

(I0)	$\emptyset \in {\mathcal {I}}\,$.
(I1)	$I\subseteq J\in {\mathcal {I}}\Rightarrow I\in {\mathcal {I}}\,$.
(I2)	$I,J\in {\mathcal {I}}\,$, $|I|<|J|\Rightarrow \exists j\in J\backslash I\,$: $I\cup \{j\}\in {\mathcal {I}}\,$.