$B_h$-sets of real and complex numbers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913721494798336 |
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| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | Let $K = \mathbb{R}$ or $\mathbb{C}$. An $n$-element subset $A$ of $K$ is a $B_h$-set if every element of $K$ has at most one representation as the sum of $h$ not necessarily distinct elements of $A$. Associated to the $B_h$ set $A = \{a_1,\ldots, a_n\}$ are the $B_h$-vectors $\mathbf{a} = (a_1,\ldots, a_n)$ in $K^n$. This paper proves that ``almost all'' $n$-element subsets of $K$ are $B_h$-sets in the sense that the set of all $B_h$-vectors is a dense open subset of $K^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $B_h$-sets of real and complex numbers Nathanson, Melvyn B. Combinatorics Number Theory 11B05, 11B13, 11B30, 11B34, 11B75, 54E52 Let $K = \mathbb{R}$ or $\mathbb{C}$. An $n$-element subset $A$ of $K$ is a $B_h$-set if every element of $K$ has at most one representation as the sum of $h$ not necessarily distinct elements of $A$. Associated to the $B_h$ set $A = \{a_1,\ldots, a_n\}$ are the $B_h$-vectors $\mathbf{a} = (a_1,\ldots, a_n)$ in $K^n$. This paper proves that ``almost all'' $n$-element subsets of $K$ are $B_h$-sets in the sense that the set of all $B_h$-vectors is a dense open subset of $K^n$. |
| title | $B_h$-sets of real and complex numbers |
| topic | Combinatorics Number Theory 11B05, 11B13, 11B30, 11B34, 11B75, 54E52 |
| url | https://arxiv.org/abs/2502.21272 |