21 阶斯泰纳三重系统的性质

Pub Date : 2024-07-15 DOI:10.1016/j.disc.2024.114158

Grahame Erskine, Terry S. Griggs

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引用次数: 0

摘要

研究了阶数为 21 的 62,336,617 个斯坦纳三系的性质，这些三系都有一个非三维自变群。其中，28 个系统没有平行类，6 个系统具有 4 色性，5 个系统具有 3 平衡性，20 个系统避开了斜边，21 个系统避开了皇冠，1 个系统避开了六边形，2 个系统避开了棱柱。所有系统都包含网格。没有一个系统的图块相交图是 3 存在封闭的。

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Properties of Steiner triple systems of order 21

Properties of the 62,336,617 Steiner triple systems of order 21 with a non-trivial automorphism group are examined. In particular, there are 28 which have no parallel class, six that are 4-chromatic, five that are 3-balanced, 20 that avoid the mitre, 21 that avoid the crown, one that avoids the hexagon and two that avoid the prism. All systems contain the grid. None have a block intersection graph that is 3-existentially closed.

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