关于重序列的重排不等式
On rearrangement inequalities for multiple sequences
摘要：
经典的重排不等式提供了两个序列的产品之和的界限下排列的条款，并表明，类似的顺序序列提供最大的值，而相反的顺序序列提供最小的值。这已经被推广到多个序列，以表明类似排序的序列提供最大值。然而，导致最小值的序列的排列通常是未知的。我们展示了一个变种的重排不等式的下界，可以获得和条件，这一界实现的序列的排列。我们还研究了一个推广的重排不等式和一个变化，其中的排列项可以跨越各种序列。对于这种变化，我们还可以在一定条件下找到最小化和极大化序列。最后，我们还研究了其他可以排序的对象（如函数和矩阵）的重排不等式。
英文摘要：
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the smallest value. This has been generalized to multiple sequences to show that similarly ordered sequences provide the largest value. However, the permutations of the sequences that result in the smallest value are generally not known. We show a variant of the rearrangement inequality for which a lower bound can be obtained and conditions for which this bound is achieved for a sequence of permutations. We also study a generalization of the rearrangement inequality and a variation where the permutations of terms can be across the various sequences. For this variation, we can also find the minimizing and maximizing sequences under certain conditions. Finally, we also look at rearrangement inequalities of other objects that can be ordered such as functions and matrices.
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