Solving a ± b = 2c in elements of finite sets

• Autorzy: Vsevolod F. Lev , Rom Pinchasi
• Języki publikacji: EN

Abstrakty

EN

We show that if A and B are finite sets of real numbers, then the number of triples (a,b,c) ∈ A × B × (A ∪ B) with a + b = 2c is at most (0.15+o(1))(|A|+|B|)² as |A| + |B| → ∞. As a corollary, if A is antisymmetric (that is, A ∩ (-A) = ∅), then there are at most (0.3+o(1))|A|² triples (a,b,c) with a,b,c ∈ A and a - b = 2c. In the general case where A is not necessarily antisymmetric, we show that the number of triples (a,b,c) with a,b,c ∈ A and a - b = 2c is at most (0.5+o(1))|A|². These estimates are sharp.

Kategorie tematyczne

• 11P70: Inverse problems of additive number theory, including sumsets
• 11B30: Arithmetic combinatorics; higher degree uniformity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 2
• Strony: 127-140

Daty

wydano

2014

Twórcy

autor

Vsevolod F. Lev

• Department of Mathematics, The University of Haifa at Oranim, Tivon 36006, Israel

autor

Rom Pinchasi

• Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

Identyfikatory

DOI

10.4064/aa163-2-3