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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2511.01073 |
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| _version_ | 1866915592409186304 |
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| author | Buratti, Marco Galici, Mario Montinaro, Alessandro Nakic, Anamari Wassermann, Alfred |
| author_facet | Buratti, Marco Galici, Mario Montinaro, Alessandro Nakic, Anamari Wassermann, Alfred |
| contents | A design is $G$-additive with $G$ an abelian group, if its points are in $G$ and each block is zero-sum in $G$. All the few known ``manageable" additive Steiner 2-designs are $\mathrm{EA}(q)$-additive for a suitable $q$, where $\mathrm{EA}(q)$ is the elementary abelian group of order $q$. We present some general constructions for $\mathrm{EA}(q)$-additive Steiner 2-designs which unify the known ones and allow to find a few new ones: an additive $\mathrm{EA}(2^8)$-additive 2-$(52,4,1)$ design which is also resolvable, and three pairwise non-isomorphic $\mathrm{EA}(3^5)$-additive 2-$(121,4,1)$ designs, none of which is the point-line design of $\mathrm{PG}(4,3)$. In the attempt to find also an $\mathrm{EA}(2^9)$-additive 2-$(511,7,1)$ design, we prove that a putative 2-analog of a 2-$(9,3,1)$ design cannot be cyclic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathrm{ EA}(q)$-additive Steiner 2-designs Buratti, Marco Galici, Mario Montinaro, Alessandro Nakic, Anamari Wassermann, Alfred Combinatorics A design is $G$-additive with $G$ an abelian group, if its points are in $G$ and each block is zero-sum in $G$. All the few known ``manageable" additive Steiner 2-designs are $\mathrm{EA}(q)$-additive for a suitable $q$, where $\mathrm{EA}(q)$ is the elementary abelian group of order $q$. We present some general constructions for $\mathrm{EA}(q)$-additive Steiner 2-designs which unify the known ones and allow to find a few new ones: an additive $\mathrm{EA}(2^8)$-additive 2-$(52,4,1)$ design which is also resolvable, and three pairwise non-isomorphic $\mathrm{EA}(3^5)$-additive 2-$(121,4,1)$ designs, none of which is the point-line design of $\mathrm{PG}(4,3)$. In the attempt to find also an $\mathrm{EA}(2^9)$-additive 2-$(511,7,1)$ design, we prove that a putative 2-analog of a 2-$(9,3,1)$ design cannot be cyclic. |
| title | $\mathrm{ EA}(q)$-additive Steiner 2-designs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.01073 |