On the dimension of additive sets

• Autorzy: P. Candela , H. A. Helfgott
• Języki publikacji: EN

Abstrakty

EN

We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of {0,1}ⁿ ⊂ ℤⁿ.

Kategorie tematyczne

• 05D40: Probabilistic methods
• 11B30: Arithmetic combinatorics; higher degree uniformity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 1
• Strony: 91-100

Daty

wydano

2015

Twórcy

autor

P. Candela

• Alfréd Rényi Institute of Mathematics, 13-15 Reáltanoda u., 1053 Budapest, Hungary

autor

H. A. Helfgott

• IMJ-PRG, UMR 7586, Bâtiment S. Germain, case 7012, 58 avenue de France, 75013 Paris, France

Identyfikatory

DOI

10.4064/aa167-1-5