The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design
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arXiv
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| Format: | Preprint |
| Publié: |
2012
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| _version_ | 1866914672583639040 |
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| author | Havlicek, Hans |
| author_facet | Havlicek, Hans |
| contents | A conic of the Veronese surface in PG(5,3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model $K$ for Witt's 5-$(12,6,1)$ design, the blocks being the hyperplane sections containing more than three (actually six) points of $K$. As such a point model is projectively unique, the present construction yields an easy coordinate-free approach to some results obtained independently by H.S.M. Coxeter and G. Pellegrino, including a projective representation of the Mathieu group $M_{12}$ in PG(5,3). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1210_2055 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design Havlicek, Hans Combinatorics 51E20 A conic of the Veronese surface in PG(5,3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model $K$ for Witt's 5-$(12,6,1)$ design, the blocks being the hyperplane sections containing more than three (actually six) points of $K$. As such a point model is projectively unique, the present construction yields an easy coordinate-free approach to some results obtained independently by H.S.M. Coxeter and G. Pellegrino, including a projective representation of the Mathieu group $M_{12}$ in PG(5,3). |
| title | The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design |
| topic | Combinatorics 51E20 |
| url | https://arxiv.org/abs/1210.2055 |