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Let \(\left \{s_{j}\right \} _{j=1}^{n}\) be positive integers. In 1959, Erd ős and Szekeres posed a number of problems about the size of polynomials of the form \(\displaystyle \Pi _{j=1}^{n}\left (1-z^{s_{j}}\right), \) where \(\left \{s_{j}\right \} _{j=1}^{n}\) are positive integers. We survey results on these problems and closely related questions.

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A Survey of Erdős-Szekeres Products

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  • 发表日期：

    2025年

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  • D. S. Lubinsky

摘要

Let \(\left \{s_{j}\right \} _{j=1}^{n}\) be positive integers. In 1959, Erd ős and Szekeres posed a number of problems about the size of polynomials of the form \(\displaystyle \Pi _{j=1}^{n}\left (1-z^{s_{j}}\right), \) where \(\left \{s_{j}\right \} _{j=1}^{n}\) are positive integers. We survey results on these problems and closely related questions.