An improved lower bound for finite additive 2-bases

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An improved lower bound for finite additive 2-bases. / Kohonen, Jukka.

In: Journal of Number Theory, Vol. 174, 05.2017, p. 518–524.

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@article{bfcdee8adb2145b381f033a6292b63e5,
title = "An improved lower bound for finite additive 2-bases",
abstract = "A set of non-negative integers A is an additive 2-basis with range n, if its sumset A+A contains 0,1,…,n but not n+1. Explicit bases are known with arbitrarily large size |A|=k and n/k²≥2/7>0.2857. We present a more general construction and improve the lower bound to 85/294>0.2891.",
keywords = "Finite additive basis, Additive number theory",
author = "Jukka Kohonen",
year = "2017",
month = "5",
doi = "10.1016/j.jnt.2016.11.011",
language = "English",
volume = "174",
pages = "518–524",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",

}

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TY - JOUR

T1 - An improved lower bound for finite additive 2-bases

AU - Kohonen, Jukka

PY - 2017/5

Y1 - 2017/5

N2 - A set of non-negative integers A is an additive 2-basis with range n, if its sumset A+A contains 0,1,…,n but not n+1. Explicit bases are known with arbitrarily large size |A|=k and n/k²≥2/7>0.2857. We present a more general construction and improve the lower bound to 85/294>0.2891.

AB - A set of non-negative integers A is an additive 2-basis with range n, if its sumset A+A contains 0,1,…,n but not n+1. Explicit bases are known with arbitrarily large size |A|=k and n/k²≥2/7>0.2857. We present a more general construction and improve the lower bound to 85/294>0.2891.

KW - Finite additive basis

KW - Additive number theory

U2 - 10.1016/j.jnt.2016.11.011

DO - 10.1016/j.jnt.2016.11.011

M3 - Article

VL - 174

SP - 518

EP - 524

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

ID: 10465054