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In the mathematical area of braid theory, the Dehornoy order is a left-invariant total order on the braid group, found by . Dehornoy's original discovery of the order on the braid group used huge cardinals, but there are now several more elementary constructions of it. ==Definition== Suppose that ''σ''1, ..., ''σ''''n''−1 are the usual generators of the braid group ''B''''n'' on ''n'' strings. The set ''P'' of positive elements in the Dehornoy order is defined to be the elements that can be written as word in the elements ''σ''1, ..., ''σ''''n''−1 and their inverses, such that for some ''i'' the word contains σ''i'' but does not contain ''σ''±1 for ''j'' < ''i'' nor ''σ''−1. The set ''P'' has the properties ''PP'' ⊆ ''P'', and the braid group is a disjoint union of ''P'', 1, and ''P''−1. These properties imply that if we define ''a'' < ''b'' to mean ''a''−1''b'' ∈ ''P'' then we get a left-invariant total order on the braid group. 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「Dehornoy order」の詳細全文を読む スポンサード リンク
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