Analysis uncovers limitations in discovering infinite patterns within sets of natural numbers, suggesting complexities in sumsets.
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found, we explore numerous open problems and obstructions to finding other infinite configurations in every set of natural numbers with positive density.
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Kra et al. (2025) studied this question.
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