• Corpus ID: 119308147

On the interplay between notions of additive and multiplicative largeness and its combinatorial applications

  title={On the interplay between notions of additive and multiplicative largeness and its combinatorial applications},
  author={Vitaly Bergelson and Daniel Glasscock},
  journal={arXiv: Combinatorics},
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic structures. We show that multiplicative largeness begets additive largeness in three ways and give a collection of examples demonstrating the optimality of these results. We also give a variety of applications arising from the connection between additive and… 
3 Citations

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