Random Finite Sum Sets and Product Sets in Subsets of the Natural Numbers
Abstract
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of N where each integer is included independently with probability p ∈ (0, 1), we prove that almost surely such a set contains finite sumsets (FS-sets) and finite product sets (FP-sets) of every finite length. Then we prove any Bernoulli random subset of N contains a pattern of the form {x, y, x + y, xy}, giving a random solution of the Hindman conjecture.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Global Integrated Mathematics
- Volume
- 2
- Issue
- 2
- Pages
- 1–12
- Publication date
- 1 July 2026
- Language
- EN