On sets of natural numbers without solution to a noninvariant linear equation

Tomasz Schoen

Acta Arithmetica (2000)

  • Volume: 93, Issue: 2, page 149-155
  • ISSN: 0065-1036

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Tomasz Schoen. "On sets of natural numbers without solution to a noninvariant linear equation." Acta Arithmetica 93.2 (2000): 149-155. <http://eudml.org/doc/207406>.

@article{TomaszSchoen2000,
author = {Tomasz Schoen},
journal = {Acta Arithmetica},
keywords = {linear equations; combinatorial number theory},
language = {eng},
number = {2},
pages = {149-155},
title = {On sets of natural numbers without solution to a noninvariant linear equation},
url = {http://eudml.org/doc/207406},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Tomasz Schoen
TI - On sets of natural numbers without solution to a noninvariant linear equation
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 2
SP - 149
EP - 155
LA - eng
KW - linear equations; combinatorial number theory
UR - http://eudml.org/doc/207406
ER -

References

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  1. [1] N. Alon, Independent sets in regular graphs and sum-free sets of finite groups, Israel J. Math. 73 (1991), 247-256. Zbl0762.05050
  2. [2] J.-M. Deshoulliers, G. Freimen, V. Sós and M. Temkin, On the structure of sum-free sets, 2, Astérisque 258 (1999), 149-161. 
  3. [3] P. Erdős, V. Sós and A. Sárközy, On sum sets of Sidon sets, J. Number Theory 47 (1993), 329-347. Zbl0811.11014
  4. [4] V. Lev, Optimal representation by sumsets and subset sums, ibid. 62 (1997), 127-143. Zbl0868.11017
  5. [5] T. Łuczak and T. Schoen, On the infinite sum-free sets of natural numbers, ibid. 66 (1997), 211-224. Zbl0884.11018
  6. [6] K. F. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. Zbl0050.04002
  7. [7] I. Z. Ruzsa, On infinite Sidon sequences, J. Number Theory 68 (1998), 63-71. Zbl0927.11005
  8. [8] I. Z. Ruzsa, Solving a linear equation in a set of integers I, Acta Arith. 65 (1993), 259-282. Zbl1042.11525
  9. [9] I. Z. Ruzsa, Solving a linear equation in a set of integers II, ibid. 72 (1995), 385-397. Zbl1044.11617
  10. [10] T. Schoen, On the density of universal sum-free sets, Combin. Probab. Comput. 8 (1999), 277-280. Zbl0936.11015
  11. [11] T. Schoen, Subsets of {1,...,n} with no solutions to the equation x+y = kz, in preparation. 

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