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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.13891 |
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Table of Contents:
- We describe in this paper additively left stable sets, i.e. sets satisfying $\left((A+A)-\inf(A)\right)\cap[\inf(A),\sup(A)]=A$ (meaning that $A-\inf(A)$ is stable by addition with itself on its convex hull), when $A$ is a finite subset of integers and when $A$ is a bounded subset of real numbers. More precisely we give a sharp upper bound for the density of $A$ in $[\inf(A),x]$ for $x\le\sup(A)$, and construct sets reaching this density for any given $x$ in this range. This gives some information on sets involved in the structural description of some critical sets in Freiman's $3k-4$ theorem in both cases.