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On Thin Sum-Product Bases

Abstract

Besides various asymptotic results on the concept of sum-product bases in the set of non-negative integers ℕ, we investigate by probabilistic arguments the existence of thin sets A, A′ of non-negative integers such that AA + A = ℕ and AA′ + AA′ = ℕ.

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Acknowledgement

We would like to thank the Referees for carefully reading the first version of this manuscript and making various suggestions to improve the expositions. We would also like to thank R. Balasubramanian, Jean-Marc Deshouillers and D. S. Ramana for various helpful discussions.

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Correspondence to Gyan Prakash.

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This paper has been prepared and written within the framework of the IFCPAR/CEFIPRA project 5401-1.

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Hennecart, F., Prakash, G. & Pramod, E. On Thin Sum-Product Bases. Combinatorica 42, 165–202 (2022). https://doi.org/10.1007/s00493-021-4195-4

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  • DOI: https://doi.org/10.1007/s00493-021-4195-4

Mathematics Subject Classification (2010)

  • 11P70