Maximal sets of numbers not containing k+1 pairwise coprime integers

Rudolf Ahlswede; Levon H. Khachatrian

Acta Arithmetica (1995)

  • Volume: 72, Issue: 1, page 77-100
  • ISSN: 0065-1036

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Rudolf Ahlswede, and Levon H. Khachatrian. "Maximal sets of numbers not containing k+1 pairwise coprime integers." Acta Arithmetica 72.1 (1995): 77-100. <http://eudml.org/doc/206786>.

@article{RudolfAhlswede1995,
author = {Rudolf Ahlswede, Levon H. Khachatrian},
journal = {Acta Arithmetica},
keywords = {density; Erdös sets; extremal sets without coprimes; maximal cardinality},
language = {eng},
number = {1},
pages = {77-100},
title = {Maximal sets of numbers not containing k+1 pairwise coprime integers},
url = {http://eudml.org/doc/206786},
volume = {72},
year = {1995},
}

TY - JOUR
AU - Rudolf Ahlswede
AU - Levon H. Khachatrian
TI - Maximal sets of numbers not containing k+1 pairwise coprime integers
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 1
SP - 77
EP - 100
LA - eng
KW - density; Erdös sets; extremal sets without coprimes; maximal cardinality
UR - http://eudml.org/doc/206786
ER -

References

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  1. [1] R. Ahlswede and L. H. Khachatrian, On extremal sets without coprimes, Acta Arith. 66 (1994), 89-99. Zbl0826.11043
  2. [2] N. G. de Bruijn, On the number of uncancelled elements in the sieve of Eratosthenes, Indag. Math. 12 (1950), 247-256. Zbl0037.03001
  3. [3] A. A. Buchstab, Asymptotische Abschätzungen einer allgemeinen zahlentheoretischen Funktion, Mat. Sb. (N.S.) 44 (1937), 1239-1246. Zbl63.0902.01
  4. [4] P. Erdős, On the density of some sequences of integers, Bull. Amer. Math. Soc. 54 (1948), 685-692. Zbl0032.01301
  5. [5] P. Erdős, Remarks in number theory IV, Mat. Lapok 13 (1962), 228-255. Zbl0127.02202
  6. [6] P. Erdős, Extremal problems in number theory, in: Theory of Numbers, Proc. Sympos. Pure Math. 8, Amer. Math. Soc., Providence, R.I., 1965, 181-189. 
  7. [7] P. Erdős, Problems and results on combinatorial number theory, Chapt. 12 in: A Survey of Combinatorial Theory, J. N. Srivastava et al. (eds.), North-Holland, 1973. 
  8. [8] P. Erdős, A survey of problems in combinatorial number theory, Ann. Discrete Math. 6 (1980), 89-115. Zbl0448.10002
  9. [9] P. Erdős and A. Sárközy, On sets of coprime integers in intervals, Hardy-Ramanujan J. 16 (1993), 1-20. 
  10. [10] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, Ann. Univ. Sci. Budapest. Eötvös 12 (1969), 131-135. Zbl0188.34504
  11. [11] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, II, Publ. Math. Debrecen 27 (1980), 117-125. Zbl0461.10047
  12. [12] R. Freud, Paul Erdős, 80-A Personal Account, Period. Math. Hungar. 26 (2) (1993), 87-93. Zbl0787.01017
  13. [13] H. Halberstam and K. F. Roth, Sequences, Oxford University Press, 1966, Springer, 1983. 
  14. [14] R. R. Hall and G. Tenenbaum, Divisors, Cambridge Tracts in Math. 90, 1988. 
  15. [15] C. Szabó and G. Tóth, Maximal sequences not containing 4 pairwise coprime integers, Mat. Lapok 32 (1985), 253-257 (in Hungarian) Zbl0609.10044

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