Article
Sumsets With Prescribed Lower and Upper Asymptotic Densities Ii
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Abstract
We show that for natural numbers h, k, such that k ≥ 2, and for real numbers α 1 , α 2, such that 0 < α 1 ≤ α 2 < 1, there exists a subset A of N = {0, 1, 2, . . .}, such that for all finite subsets B of N such that max B − min B = h, the lower and upper asymptotic densities of kA + B are α 1 and α 2, respectively.
Keywords
asymptotic density, sumsets.
Citation
Grekos, G., Krishna Pandey, R., & Teja Somu, S. (2024). Sumsets with prescribed lower and upper asymptotic densities ii. Uniform Distribution Theory, 19(1), 92–102. https://doi.org/10.2478/UDT-2024-0007
G. Grekos, R. Krishna Pandey and S. Teja Somu, “Sumsets with prescribed lower and upper asymptotic densities ii,” Uniform Distribution Theory, vol. 19, no. 1, pp. 92–102, 2024, doi: 10.2478/UDT-2024-0007.
Grekos G, Krishna Pandey R, Teja Somu S. Sumsets with prescribed lower and upper asymptotic densities ii. Uniform Distribution Theory. 2024;19(1):92–102. doi:10.2478/UDT-2024-0007.
Grekos, G., Krishna Pandey, R. and Teja Somu, S. (2024), ‘Sumsets with prescribed lower and upper asymptotic densities ii’, Uniform Distribution Theory, 19(1), pp. 92–102. Available at: https://doi.org/10.2478/UDT-2024-0007.
Grekos, Georges, et al. “Sumsets with Prescribed Lower and Upper Asymptotic Densities Ii.” Uniform Distribution Theory, vol. 19, no. 1, 2024, pp. 92–102. https://doi.org/10.2478/UDT-2024-0007.
Grekos, Georges, Ram Krishna Pandey, and Sai Teja Somu. “Sumsets with Prescribed Lower and Upper Asymptotic Densities Ii.” Uniform Distribution Theory 19, no. 1 (2024): 92–102. https://doi.org/10.2478/UDT-2024-0007.
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- DOI: 10.2478/udt-2024-0007
- Type: article
- Source: Uniform distribution theory
- Published: 2024-12-01
- OpenAlex ID: W4403713487
Published by: Engineering Journals
