Addition theorems in partially ordered groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909597885792256 |
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| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially ordered abelian and nonabelian groups. One abelian application is an addition theorem for sums of sets of $n$-dimensional lattice points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Addition theorems in partially ordered groups Nathanson, Melvyn B. Number Theory Group Theory 05E16, 06A17, 06F05, 06F15, 06F20, 11B05, 11B13, 11B75, 11P21, 11P70 Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially ordered abelian and nonabelian groups. One abelian application is an addition theorem for sums of sets of $n$-dimensional lattice points. |
| title | Addition theorems in partially ordered groups |
| topic | Number Theory Group Theory 05E16, 06A17, 06F05, 06F15, 06F20, 11B05, 11B13, 11B75, 11P21, 11P70 |
| url | https://arxiv.org/abs/2409.16233 |