有关两个序列重新排列的一个问题

A renumbering problem of two sequences

设（ｘ）与（ｙ）是任意两个同具ｎ项的实数序列，对（ｘ）与（ｙ）的所有重新排列（ｘ′）与（ｙ′），考虑诸和式∑ｘ′ｙ′之间的比较问题．通过引进ｎ次对称群Ｓｎ上的一个偏序，将和式的比较转化为排列在该序意义下的比较；给出了可比较的若干充分必要条件；指出了此序正是Ｓｎ上的Ｂｒｕｈａｔ序的对偶．

A partial order on the symmetric group Sn is introduced to answer the question of how to compare values of ∑xy for all renumbering of sequences (x) and (y) with n real numbers separately. The authors present some characterizations of this order, and then conclude that this order is just the dual of the Bruhat order on Sn.