There is No McLaughlin Geometry
| Autor: | Östergård, Patric R. J., Soicher, Leonard H. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We determine that there is no partial geometry ${\cal G}$ with parameters $(s,t,\alpha)=(4,27,2)$. The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest in ${\cal G}$ is due to the fact that it would have the exceptional McLaughlin graph as its point graph. Our proof makes extensive use of symmetry and high-performance distributed computing, and details of our techniques and checks are provided. One outcome of our work is to show that a pseudogeometric strongly regular graph achieving equality in the Krein bound need not be the point graph of any partial geometry. Comment: 19 pages |
| Databáze: | arXiv |
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