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On Thin Sum-Product Bases

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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 A′A′ + A′A′ = 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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Authors and Affiliations

  1. UJM-Saint-Étienne CNRS, ICJ UMR 5208, Univ. Lyon, 42023, Saint-Étienne, France

    François Hennecart

  2. Harish-Chandra Research Institute HBNI, Jhunsi, Prayagraj (Allahabad), 211 019, India

    Gyan Prakash & Eyyunni Pramod

Authors
  1. François Hennecart
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  2. Gyan Prakash
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  3. Eyyunni Pramod
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Corresponding author

Correspondence to Gyan Prakash.

Additional information

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

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