Infinite Sumsets in Sets with Positive Density
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911781620809728 |
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| author | Kra, Bryna Moreira, Joel Richter, Florian K. Robertson, Donald |
| author_facet | Kra, Bryna Moreira, Joel Richter, Florian K. Robertson, Donald |
| contents | Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of $k=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_01786 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Infinite Sumsets in Sets with Positive Density Kra, Bryna Moreira, Joel Richter, Florian K. Robertson, Donald Dynamical Systems Combinatorics Number Theory 05D10 11B13 37A05 11B30 Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of $k=2$. |
| title | Infinite Sumsets in Sets with Positive Density |
| topic | Dynamical Systems Combinatorics Number Theory 05D10 11B13 37A05 11B30 |
| url | https://arxiv.org/abs/2206.01786 |