Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.01301 |
| Tags: |
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Sommario:
- We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability $p\in (0,1)$, we prove that almost surely such a set contains finite sumsets (FS-sets) and finite product sets (FP-sets) of every finite length. In addition, we establish a novel connection between Hindman's partition theorem and the central limit theorem, providing a probabilistic perspective on the asymptotic Gaussian behavior of monochromatic finite sums and products. These results can be interpreted as probabilistic analogues of finite-dimensional versions of Hindman's theorem. Applications, implications, and open questions related to infinite FS-sets and FP-sets are discussed.