This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica 16(1973), 157–176.
E. Cohen, The number of representations of an integer as the sum of two square-free numbers, Duke Math. J. 32(1965), 181–185.
J.-M. Deshouillers and G. Grekos, Non-bases additives maximales, preprint.
P. Erdös, Einige Bemerkungen zur Arbeit von A. Stöhr, "Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe," J. Reine Angew. Math. 197(1957), 216–219.
P. Erdös and E. Härtter, Konstruktion von nichtperiodischen Minimalbasen mit der Dichte 1/2 für die Menge der nichtnegativen ganzen Zahlen, J. Reine Angew. Math. 221(1966), 44–47.
P. Erdös and M. B. Nathanson, Maximal asymptotic nonbases, Proc. Amer. Math. Soc. 48(1975), 57–60.
P. Erdös and M. B. Nathanson, Oscillations of bases for the natural numbers, Proc. Amer. Math. Soc. 53(1975), 253–258.
P. Erdös and M. B. Nathanson, Partitions of the natural numbers into infinitely oscillating bases and nonbases, Comment. Math. Helvet. 51(1976), 171–182.
P. Erdös and M. B. Nathanson, Nonbases of density zero not contained in maximal nonbases, J. London Math. Soc. 15(1977), 403–405.
P. Erdös and M. B. Nathanson, Sets of natural numbers with no minimal asymptotic bases, Proc. Amer. Math. Soc. 70(1978), 100–102.
P. Erdös and M. B. Nathanson, Bases and nonbases of squarefree integers, J. Number Theory, to appear.
P. Erdös and M. B. Nathanson, Minimal asymptotic bases for the natural numbers, J. Number Theory, to appear.
P. Erdös and A. Rényi, Additive properties of random sequences of positive integers, Acta Arith. 6(1960), 83–110.
T. Estermann, On the representation of a number as the sum of two numbers not divisible by k-th powers, J. London Math. Soc. 6 (1931), 37–40.
C. J. A. Evelyn and E. H. Linfoot, On a problem in the additive theory of numbers, II, J. für Math. 164(1931), 131–140.
H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974.
H. Halberstam and K. F. Roth, Sequences, Vol. 1, Oxford University Press, Oxford, 1966.
E. Härtter, Ein Beitrag zur Theorie der Minimalbasen, J. Reine Angew. Math. 196(1956), 170–204.
E. Härtter, Eine Bemerkung uber periodische Minimalbasen für die Menge der nichtnegativen ganzen Zahlen, J. Reine Angew. Math. 214/215(1964), 395–398.
J. Hennefeld, Asymptotic nonbases not contained in maximal asymptotic nonbases, Proc. Amer. Math. Soc. 62(1977), 23–24.
M. B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6(1974), 324–333.
M. B. Nathanson, s-maximal nonbases of density zero, J. London Math. Soc. 15(1977), 29–34.
M. B. Nathanson, Oscillations of bases in number theory and combinatorics, in: Number Theory Day, Springer-Verlag Lecture Notes in Mathematics, Vol. 626, 1977, pp. 217–231.
A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe, J. Reine Angew. Math. 194(1955), 40–65, 111–140.
E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arithmetica 27(1975), 199–245.
S. Turjányi, On maximal asymptotic nonbases of density zero, J. Number Theory 9(1977), 271–275.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this chapter
Cite this chapter
Erdös, P., Nathanson, M.B. (1979). Systems of distinct representatives and minimal bases in additive number theory. In: Nathanson, M.B. (eds) Number Theory Carbondale 1979. Lecture Notes in Mathematics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062704
Download citation
DOI: https://doi.org/10.1007/BFb0062704
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09559-0
Online ISBN: 978-3-540-34852-8
eBook Packages: Springer Book Archive
