论文标题
部分可观测时空混沌系统的无模型预测
On the two-distance embedding in real Euclidean space of coherent configuration of type (2,2;3)
论文作者
论文摘要
在欧几里得空间中找到$ 2 $持续设置的最大基数是几何问题的经典问题。 1997年的Lisoněk构建了$ \ Mathbb r^8 $的最高$ 2 $ - 持续设置，$ 45 $。 Lisoněk构建的$ 2 $ distance集具有$（2,2; 3）$类型的连贯配置的杰出结构，并嵌入了两个同心球中，以$ \ Mathbb r^8 $。在本文中，我们研究了是否存在类型$（2,2; 3）$的连贯配置的其他类似嵌入为$ 2 $ distance in $ \ mathbb r^n $中的$ 2 $ distance，而无需假设对集合的大小进行任何限制。我们证明，除了Lisoněk之外，没有其他例子。我们证明的关键思想如下：（i）研究欧几里得空间中相干构型的嵌入的几何形状，并驱动来自这种嵌入的二聚体方程。 （ii）通过使用辅助方程的方法，求解具有组合结构某些参数的某些正成状态的二氧化苯胺方程。
Finding the maximum cardinality of a $2$-distance set in Euclidean space is a classical problem in geometry. Lisoněk in 1997 constructed a maximum $2$-distance set in $\mathbb R^8$ with $45$ points. That $2$-distance set constructed by Lisoněk has a distinguished structure of a coherent configuration of type $(2,2;3)$ and is embedded in two concentric spheres in $\mathbb R^8$. In this paper we study whether there exists any other similar embedding of a coherent configuration of type $(2,2;3)$ as a $2$-distance set in $\mathbb R^n$, without assuming any restriction on the size of the set. We prove that there exists no such example other than that of Lisoněk. The key ideas of our proof are as follows: (i) study the geometry of the embedding of the coherent configuration in Euclidean spaces and to drive diophantine equations coming from this embedding. (ii) solve diophantine equations with certain additional conditions of integrality of some parameters of the combinatorial structure by using the method of auxiliary equations.
