The existence of pyramidal Steiner triple systems over abelian groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910191131295744 |
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| author | Chang, Yanxun Traetta, Tommaso Zhou, Junling |
| author_facet | Chang, Yanxun Traetta, Tommaso Zhou, Junling |
| contents | A Steiner triple system STS$(v)$ is called $f$-pyramidal if it has an automorphism group fixing $f$ points and acting sharply transitively on the remaining $v-f$ points. In this paper, we focus on the STSs that are $f$-pyramidal over some abelian group. Their existence has been settled only for the smallest admissible values of $f$, that is, $f=0,1,3$.
In this paper, we complete this result and determine, for every $f>3$, the spectrum of values $(f,v)$ for which there is an $f$-pyramidal STS$(v)$ over an abelian group. This result is obtained by constructing difference families relative to a suitable partial spread. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The existence of pyramidal Steiner triple systems over abelian groups Chang, Yanxun Traetta, Tommaso Zhou, Junling Combinatorics 05B07, 20B25 A Steiner triple system STS$(v)$ is called $f$-pyramidal if it has an automorphism group fixing $f$ points and acting sharply transitively on the remaining $v-f$ points. In this paper, we focus on the STSs that are $f$-pyramidal over some abelian group. Their existence has been settled only for the smallest admissible values of $f$, that is, $f=0,1,3$. In this paper, we complete this result and determine, for every $f>3$, the spectrum of values $(f,v)$ for which there is an $f$-pyramidal STS$(v)$ over an abelian group. This result is obtained by constructing difference families relative to a suitable partial spread. |
| title | The existence of pyramidal Steiner triple systems over abelian groups |
| topic | Combinatorics 05B07, 20B25 |
| url | https://arxiv.org/abs/2501.07928 |