  Propositions 1.1 -- 1.3 stated below contribute to results and certain
problems considered in a paper by Erdos and Szekeres, on the behavior of
products $\prod^n_1 (1-z^{a_j}), 1\leq a_1\leq \cdots\leq a_n$ integers. In the
discussion, $\{a_1, \ldots, a_n \}$ will be either a proportional subset of
$\{1, \ldots, n\}$ or a set of large arithmetic diameter.
