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

• Autorzy: Tomasz Schoen
• Języki publikacji: EN

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 11A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 2
• Strony: 149-155

Daty

wydano

2000

otrzymano

1999-06-18

poprawiono

1999-12-06

Twórcy

autor

Tomasz Schoen

• Mathematisches Seminar, Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany

Bibliografia

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