On a paper of Erd\"os and Szekeres
Mei-Chu Chang, Jean Bourgain

TL;DR
This paper extends Erdös and Szekeres' work on the behavior of specific products involving integer sequences, providing new propositions that deepen understanding of their properties in relation to proportional subsets and sets with large arithmetic diameter.
Contribution
It introduces new propositions that advance the analysis of products of the form \\prod_{j=1}^n (1 - z^{a_j}) in the context of Erdös and Szekeres' problems, focusing on particular integer sets.
Findings
Propositions 1.1 -- 1.3 offer new insights into product behavior.
Results relate to proportional subsets of \\{1, ..., n\\}.
Results also address sets with large arithmetic diameter.
Abstract
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 integers. In the discussion, will be either a proportional subset of or a set of large arithmetic diameter.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Analytic Number Theory Research · Advanced Banach Space Theory
