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In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. first studied order dimension; for a more detailed treatment of this subject than provided here, see . ==Formal definition== The dimension of a poset ''P'' is the least integer ''t'' for which there exists a family : of linear extensions of ''P'' so that, for every ''x'' and ''y'' in ''P'', ''x'' precedes ''y'' in ''P'' if and only if it precedes ''y'' in each of the linear extensions. That is, : An alternative definition of order dimension is as the minimal number of total orders such that ''P'' embeds to the product of these total orders for the componentwise ordering, in which if and only if for all ''i'' (, ). 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「order dimension」の詳細全文を読む スポンサード リンク
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