The Typical Approximate Structure of Sets with Bounded Sumset
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Bibliographic record
Abstract
Let and be randomly chosen subsets of the first positive integers of cardinalities , such that their sumset has size . We show that asymptotically almost surely and are almost fully contained in arithmetic progressions and with the same common difference and cardinalities approximately . We also prove a counting theorem for such pairs of sets in arbitrary abelian groups. The results hold for and . Our main tool is an asymmetric version of the method of hypergraph containers which was recently used by Campos to prove similar results in the special case .
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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