  We characterize the sequences $(w_i)_{i=1}^\infty$ of non-negative numbers
for which \[ \sum_{i=1}^\infty a_i w_i \quad \text{ is of the same order as }
\quad \sup_n \sum_{i=1}^n a_i w_{1+n-i} \] when $(a_i)_{i=1}^\infty$ runs over
all non-increasing sequences of non-negative numbers. As a by-product of our
work we settle a problem raised in [F. Albiac, Jose L. Ansorena and B. Wallis;
arXiv:1703.07772[math.FA]] and prove that Garling sequences spaces have no
symmetric basis.
