The decreasing rearrangement of a finite sequence a
1, a
2, … , an
of real numbers is a second sequence a
π(1), a
π(2), … , aπ(n)
, where π(l), π(2), … , π(n) is a permutation of 1, 2, … , n and
(1, p. 260). The kth term of the rearranged sequence will be denoted by . Thus the terms of the rearranged sequence correspond to and are equal to those of the given sequence ak, but are arranged in descending (non-increasing) order.