An explicit economical additive basis
Abstract We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots \}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon \gt 0$ , \begin{equation*}\lim _{N\to \infty }\frac {\big |\big \{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big \}\big |}{N^{\varepsilon }} = 0.\end{equation*} This answers a question of Erdős.
Authors
- Mehtaab Sawhney (ORCID: https://orcid.org/0009-0002-3238-7134)
- Dmitrii Zakharov
- Vishesh Jain
- Huy Tuan Pham
Institutions
- University of Illinois Chicago (US)
- Massachusetts Institute of Technology (US)
- Columbia University (US)
- Stanford University (US)
Publication Details
- Journal
- Combinatorics Probability Computing
- Published
- 2025-09-12
- DOI
- https://doi.org/10.1017/s096354832510014x
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00