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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12412 |
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| _version_ | 1866909293578551296 |
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| author | Buratti, Marco Pasotti, Anita |
| author_facet | Buratti, Marco Pasotti, Anita |
| contents | A $(v,k;r)$ Heffter space is a resolvable $(v_r,b_k)$ configuration whose points form a half-set of an abelian group $G$ and whose blocks are all zero-sum in $G$. It was recently proved that there are infinitely many orders $v$ for which, given any pair $(k,r)$ with $k\geq3$ odd, a $(v,k;r)$ Heffter space exists. This was obtained by imposing a point-regular automorphism group. Here we relax this request by asking for a point-semiregular automorphism group. In this way the above result is extended also to the case $k$ even. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More Heffter Spaces via finite fields Buratti, Marco Pasotti, Anita Combinatorics A $(v,k;r)$ Heffter space is a resolvable $(v_r,b_k)$ configuration whose points form a half-set of an abelian group $G$ and whose blocks are all zero-sum in $G$. It was recently proved that there are infinitely many orders $v$ for which, given any pair $(k,r)$ with $k\geq3$ odd, a $(v,k;r)$ Heffter space exists. This was obtained by imposing a point-regular automorphism group. Here we relax this request by asking for a point-semiregular automorphism group. In this way the above result is extended also to the case $k$ even. |
| title | More Heffter Spaces via finite fields |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.12412 |