Oriented Steiner Triple Systems, Steiner Products, and Dynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912478951112704 |
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| author | Kettinger, Jake Peterson, Chris |
| author_facet | Kettinger, Jake Peterson, Chris |
| contents | Let S denote a Steiner triple system on an n-element set. An orientation of S is an assignment of a cyclic ordering to each of the triples in S. From an oriented Steiner triple system, one can define an anticommutative bilinear operation on Rn resembling the cross product. We call this bilinear operation a Steiner product. We classify the oriented Steiner triple systems on sets of size 7 and 9 and investigate the dynamics of their associated Steiner products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Oriented Steiner Triple Systems, Steiner Products, and Dynamics Kettinger, Jake Peterson, Chris Combinatorics Rings and Algebras Let S denote a Steiner triple system on an n-element set. An orientation of S is an assignment of a cyclic ordering to each of the triples in S. From an oriented Steiner triple system, one can define an anticommutative bilinear operation on Rn resembling the cross product. We call this bilinear operation a Steiner product. We classify the oriented Steiner triple systems on sets of size 7 and 9 and investigate the dynamics of their associated Steiner products. |
| title | Oriented Steiner Triple Systems, Steiner Products, and Dynamics |
| topic | Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2507.09396 |