浅排列是未链接的排列
The shallow permutations are the unlinked permutations
摘要：
Diaconis和格雷厄姆研究了距离的措施，从身份的对称群称为总位移，并表明，它是有界的总和以下的长度和反射长度。他们要求一个特征的排列，这个界限是一个平等的;我们称之为浅排列。Cornwell和McNew最近将置换的循环图解释为纽结图，并研究了对应的链接是未链接的置换的集合。我们证明了浅置换恰好是非链接置换。正如Cornwell和McNew给出了一个计算非链接排列的生成函数，这给出了一个计算浅排列的生成函数。
英文摘要：
Diaconis and Graham studied a measure of distance from the identity in the symmetric group called total displacement and showed that it is bounded below by the sum of length and reflection length. They asked for a characterization of the permutations where this bound is an equality; we call these the shallow permutations. Cornwell and McNew recently interpreted the cycle diagram of a permutation as a knot diagram and studied the set of permutations for which the corresponding link is an unlink. We show the shallow permutations are precisely the unlinked permutations. As Cornwell and McNew give a generating function counting unlinked permutations, this gives a generating function counting shallow permutations.
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