论文标题
关于多个序列的重排不平等
On rearrangement inequalities for multiple sequences
论文作者
论文摘要
经典的重排不平等为两个术语排列下两个序列的产物的总和提供了界限，并表明类似有序的序列提供了最大的值，而相反的有序序列则提供了最小的值。已将其推广到多个序列，以表明类似有序的序列提供了最大的值。但是，导致最小值的序列的排列通常不知道。我们显示了重排不等式的变体，可以为此获得下限，并为一系列排列序列实现这种结合的条件。我们还研究了重排不平等的概括和术语排列可以在各个序列之间进行的变化。对于这种变化，我们还可以在某些条件下找到最小化和最大化序列。最后，我们还考虑了可以订购的其他物体（例如函数和矩阵）的重新排列不平等。
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.
