Maximizing the number of rational-value sums or zero-sums
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908556107710464 |
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| author | Móricz, Benjamin Nagy, Zoltán Lóránt |
| author_facet | Móricz, Benjamin Nagy, Zoltán Lóránt |
| contents | What is the maximum number of $r$-term sums admitting rational values in $n$-element sets of irrational numbers? We determine the maximum when $r<4$ or $r\geq n/2$ and also in case when we drop the condition on the number of summands. It turns out that the $r$-term sum problem is equivalent to determine the maximum number of $r$-term zero-sum subsequences in $n$-element sequences of integers, which can be seen as a variant of the famous Erdős-Ginzburg-Ziv theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximizing the number of rational-value sums or zero-sums Móricz, Benjamin Nagy, Zoltán Lóránt Combinatorics Number Theory What is the maximum number of $r$-term sums admitting rational values in $n$-element sets of irrational numbers? We determine the maximum when $r<4$ or $r\geq n/2$ and also in case when we drop the condition on the number of summands. It turns out that the $r$-term sum problem is equivalent to determine the maximum number of $r$-term zero-sum subsequences in $n$-element sequences of integers, which can be seen as a variant of the famous Erdős-Ginzburg-Ziv theorem. |
| title | Maximizing the number of rational-value sums or zero-sums |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2411.04449 |