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SOME REMARKS ON MINIMAL ASYMPTOTIC BASES OF ORDER THREE

Part of: Sequences and sets

Published online by Cambridge University Press:  08 January 2020

DENGRONG LING  and
MIN TANG
DENGRONG LING
Affiliation:
School of Mathematics and Statistics, Anhui Normal University, Wuhu241003, PR China email [email protected]
MIN TANG*
Affiliation:
School of Mathematics and Statistics, Anhui Normal University, Wuhu241003, PR China email [email protected]
*
✉[email protected]
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Abstract

We study a question on minimal asymptotic bases asked by Nathanson [‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532].

Keywords

asymptotic basisminimal asymptotic basis

MSC classification

Primary: 11B13: Additive bases, including sumsets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 21 - 30
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by the National Natural Science Foundation of China, Grant No. 11971033, and the Natural Science Foundation of Anhui Normal University, Grant No. 2017XJJ45.

References

Chen, F. J. and Chen, Y. G., ‘On minimal asymptotic bases’, European J. Combin. 32 (2011), 1329–1335.10.1016/j.ejc.2011.06.002CrossRefGoogle Scholar
Chen, Y. G. and Tang, M., ‘On a problem of Nathanson’, Acta Arith. 185 (2018), 275–280.10.4064/aa171031-26-4CrossRefGoogle Scholar
Jia, X. D. and Nathanson, M. B., ‘A simple construction of minimal asymptotic bases’, Acta Arith. 51 (1989), 95–101.10.4064/aa-52-2-95-101CrossRefGoogle Scholar
Lee, J. B., ‘A construction of minimal asymptotic bases’, Period. Math. Hungar. 26 (1993), 211–218.10.1007/BF01875975CrossRefGoogle Scholar
Ling, D. R. and Tang, M., ‘On minimal asymptotic g-adic bases’, Bull. Aust. Math. Soc. 92 (2015), 374–379.CrossRefGoogle Scholar
Ling, D. R. and Tang, M., ‘On minimal asymptotic bases of order three’, Colloq. Math. 151 (2018), 9–18.CrossRefGoogle Scholar
Nathanson, M. B., ‘Minimal bases and maximal nonbases in additive number theory’, J. Number Theory 6 (1974), 324–333.10.1016/0022-314X(74)90028-6CrossRefGoogle Scholar
Nathanson, M. B., ‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532.CrossRefGoogle Scholar
Sun, C. F., ‘On minimal asymptotic basis of order g - 1’, Indag. Math. 30 (2019), 128–135.CrossRefGoogle Scholar