On finite additive $2$-bases
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- by Laurent Habsieger PDF
- Trans. Amer. Math. Soc. 366 (2014), 6629-6646 Request permission
Abstract:
For a positive integer $N$, a set $\mathcal {B}$ of integers from $\{0,1,\dots ,N-1\}$ is called an additive $2$-basis for $N$ if every integer $n\in \{0,1,\dots ,N-1\}$ may be represented as the sum of $2$ elements of $\mathcal {B}$. We discuss the methods used to estimate the minimal size of an additive $2$-basis for $N$. We provide new examples to enrich this survey, which give good bounds. For instance, we slightly improve on the current record, from $0.46972$ to $0.46906$.References
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Additional Information
- Laurent Habsieger
- Affiliation: Centre de Recherches Mathématiques, CNRS UMI 3457, Université de Montréal, Case Postale 6128, Succursale Centre-Ville, Montréal, Quebec, Canada H3C 3J7
- Email: habsieger@CRM.UMontreal.ca
- Received by editor(s): April 15, 2013
- Published electronically: July 17, 2014
- Additional Notes: This work was supported by the French National Agency for Research (CAESAR ANR-12-BS01-0011). The author also thanks Alain Plagne and Victor Lambert for their careful reading of a preliminary version of this paper.
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 366 (2014), 6629-6646
- MSC (2010): Primary 11B13; Secondary 11B34
- DOI: https://doi.org/10.1090/S0002-9947-2014-06357-5
- MathSciNet review: 3267021