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In order theory, a branch of mathematics, a linear extension of a partial order is a linear order (or total order) that is compatible with the partial order. As a classic example, the lexicographic order of totally ordered sets is a linear extension of their product order. ==Definitions== Given any partial orders ≤ and ≤ * on a set ''X'', ≤ * is a linear extension of ≤ exactly when (1) ≤ * is a linear order and (2) for every ''x'' and ''y'' in ''X'', if , then . It is that second property that leads mathematicians to describe ≤ * as extending ≤. Alternatively, a linear extension may be viewed as an order-preserving bijection from a partially ordered set ''P'' to a chain ''C'' on the same ground set. 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「Linear extension」の詳細全文を読む スポンサード リンク
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