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Large sets in $\mathbb{N}$ have strong combinatorial structures. For example, it is known that central sets in $\mathbb{N}$ contain arbitrarily long arithmetic progressions. It also contains solutions to all partition regular systems of homogeneous linear equations.

My question: Are there any real-world research applications of all this methodology? Can anyone suggest me any book or research articles where I will get the real world application of Large sets, such as syndetic sets, central sets, etc?

Thank you in advance. Any help will be appreciated.

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    $\begingroup$ What, to you, counts as a "real-world application"? $\endgroup$
    – Alex Kruckman
    Commented Jun 25, 2023 at 20:52
  • $\begingroup$ @AlexKruckman: I understand that the question is a bit vague. Honestly, I would like to understand the applications in computer science, artificial intelligence, etc. Maybe the question is not making any sense. If it does, please provide some references for these kinds of papers. $\endgroup$
    – Arpita Ghosh
    Commented Jul 1, 2023 at 9:01

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