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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2503.18101 |
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| _version_ | 1866909742439333888 |
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| author | Costa, Simone Della Fiore, Stefano Engel, Eva R. |
| author_facet | Costa, Simone Della Fiore, Stefano Engel, Eva R. |
| contents | A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Bedert and Kravitz proved that this statement holds whenever $|A| \leq e^{c(\log p)^{1/4}}$.
In this paper, we will use a similar procedure to obtain an upper bound of the same type in the case of semidirect products $\mathbb{Z}_p \rtimes_φ H$ where $φ: H \to Aut(\mathbb{Z}_p)$ satisfies $φ(h) \in \{id, -id\}$ for each $h \in H$ and where $H$ is abelian and each subset of $H$ can be ordered such that all of its partial products are distinct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graham's rearrangement for a class of semidirect products Costa, Simone Della Fiore, Stefano Engel, Eva R. Combinatorics A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Bedert and Kravitz proved that this statement holds whenever $|A| \leq e^{c(\log p)^{1/4}}$. In this paper, we will use a similar procedure to obtain an upper bound of the same type in the case of semidirect products $\mathbb{Z}_p \rtimes_φ H$ where $φ: H \to Aut(\mathbb{Z}_p)$ satisfies $φ(h) \in \{id, -id\}$ for each $h \in H$ and where $H$ is abelian and each subset of $H$ can be ordered such that all of its partial products are distinct. |
| title | Graham's rearrangement for a class of semidirect products |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.18101 |