On the number of small Steiner triple systems with Veblen points
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915094252748800 |
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| author | Galici, Mario Filippone, Giuseppe |
| author_facet | Galici, Mario Filippone, Giuseppe |
| contents | The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for v>21. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of small Steiner triple systems with Veblen points Galici, Mario Filippone, Giuseppe Combinatorics Group Theory 05B07, 20N05, 51E10 The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for v>21. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples. |
| title | On the number of small Steiner triple systems with Veblen points |
| topic | Combinatorics Group Theory 05B07, 20N05, 51E10 |
| url | https://arxiv.org/abs/2411.16307 |