Finer control on relative sizes of iterated sumsets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909640943468544 |
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| author | Fox, Jacob Kravitz, Noah Zhang, Shengtong |
| author_facet | Fox, Jacob Kravitz, Noah Zhang, Shengtong |
| contents | Inspired by recent questions of Nathanson, we show that for any infinite abelian group $G$ and any integers $m_1, \ldots, m_H$, there exist finite subsets $A,B \subseteq G$ such that $|hA|-|hB|=m_h$ for each $1 \leq h \leq H$. We also raise, and begin to address, questions about the smallest possible cardinalities and diameters of such sets $A,B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finer control on relative sizes of iterated sumsets Fox, Jacob Kravitz, Noah Zhang, Shengtong Combinatorics Inspired by recent questions of Nathanson, we show that for any infinite abelian group $G$ and any integers $m_1, \ldots, m_H$, there exist finite subsets $A,B \subseteq G$ such that $|hA|-|hB|=m_h$ for each $1 \leq h \leq H$. We also raise, and begin to address, questions about the smallest possible cardinalities and diameters of such sets $A,B$. |
| title | Finer control on relative sizes of iterated sumsets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.05691 |