# Independence of solution sets and minimal asymptotic bases

Paul Erdős; Melvyn B. Nathanson; Prasad Tetali

Acta Arithmetica (1995)

- Volume: 69, Issue: 3, page 243-258
- ISSN: 0065-1036

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top## How to cite

topPaul Erdős, Melvyn B. Nathanson, and Prasad Tetali. "Independence of solution sets and minimal asymptotic bases." Acta Arithmetica 69.3 (1995): 243-258. <http://eudml.org/doc/206686>.

@article{PaulErdős1995,

author = {Paul Erdős, Melvyn B. Nathanson, Prasad Tetali},

journal = {Acta Arithmetica},

keywords = {minimal asymptotic bases; restricted asymptotic bases},

language = {eng},

number = {3},

pages = {243-258},

title = {Independence of solution sets and minimal asymptotic bases},

url = {http://eudml.org/doc/206686},

volume = {69},

year = {1995},

}

TY - JOUR

AU - Paul Erdős

AU - Melvyn B. Nathanson

AU - Prasad Tetali

TI - Independence of solution sets and minimal asymptotic bases

JO - Acta Arithmetica

PY - 1995

VL - 69

IS - 3

SP - 243

EP - 258

LA - eng

KW - minimal asymptotic bases; restricted asymptotic bases

UR - http://eudml.org/doc/206686

ER -

## References

top- [1] P. Erdős and M. B. Nathanson, Oscillations of bases for the natural numbers, Proc. Amer. Math. Soc. 53 (1975), 253-258. Zbl0319.10066
- [2] P. Erdős and M. B. Nathanson, Independence of solution sets in additive number theory, in: Probability, Statistical Mechanics, and Number Theory, G.-C. Rota (ed.), Adv. Math. Suppl. Stud. 9 (1986), 97-105.
- [3] P. Erdős and M. B. Nathanson, Systems of distinct representatives and minimal bases in additive number theory, in: Number Theory, Carbondale 1979, M. B. Nathanson (ed.), Lecture Notes in Math. 751, Springer, Heidelberg, 1979, 89-107.
- [4] P. Erdős and M. B. Nathanson, Problems and results on minimal bases in additive number theory, in: Number Theory, New York 1985-86, D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn, and M. B. Nathanson (eds.), Lecture Notes in Math. 1240, Springer, Heidelberg, 1987, 87-96.
- [5] P. Erdős and R. Rado, Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85-90. Zbl0103.27901
- [6] P. Erdős and A. Rényi, Additive properties of random sequences of positive integers, Acta Arith. 6 (1960), 83-110. Zbl0091.04401
- [7] P. Erdős and P. Tetali, Representations of integers as the sum of k terms, Random Structures and Algorithms 1 (1990), 245-261. Zbl0725.11007
- [8] H. Halberstam and K. F. Roth, Sequences, Springer, Heidelberg, 1983.
- [9] X.-D. Jia, Simultaneous systems of representatives for finite families of finite sets, Proc. Amer. Math. Soc. 104 (1988), 33-36. Zbl0662.10041
- [10] M. B. Nathanson, Simultaneous systems of representatives for families of finite sets, Proc. Amer. Math. Soc. 103 (1988), 1322-1326. Zbl0709.05006

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