Asymptotic nonbases which are not subsets of maximal asymptotic nonbases
HTML articles powered by AMS MathViewer
- by Julien Hennefeld PDF
- Proc. Amer. Math. Soc. 62 (1977), 23-24 Request permission
Abstract:
Let A be a set of positive integers. If all but a finite number of the positive integers can be written as a sum of h elements of A, then A is called an asymptotic basis of order h. Otherwise, A is called an asymptotic nonbasis of order h. For each $h \geqslant 2$, we construct an asymptotic nonbasis of order h which is not a subset of a maximal asymptotic nonbasis of order h.References
- Paul Erdős and Melvyn B. Nathanson, Maximal asymptotic nonbases, Proc. Amer. Math. Soc. 48 (1975), 57–60. MR 357363, DOI 10.1090/S0002-9939-1975-0357363-0
- Paul Erdős and Melvyn B. Nathanson, Oscillations of bases for the natural numbers, Proc. Amer. Math. Soc. 53 (1975), no. 2, 253–258. MR 384739, DOI 10.1090/S0002-9939-1975-0384739-8
- Melvyn B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6 (1974), 324–333. MR 347764, DOI 10.1016/0022-314X(74)90028-6
- Alfred Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. I, II, J. Reine Angew. Math. 194 (1955), 40–65, 111–140 (German). MR 75228, DOI 10.1515/crll.1955.194.40
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 23-24
- MSC: Primary 10L05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0506141-X
- MathSciNet review: 0506141