论文标题
在Johnson $ \ Mathcal {J}（n，k）$图上由粒子系统诱导的简单图上诱导的图
On sub-graphs of the Johnson $\mathcal{J}(n,k)$ graph induced by particle systems on simple graphs
论文作者
论文摘要
事实证明，了解状态空间的拓扑对于具有连续状态空间的动态系统非常有效。另一方面，对于有限简单图的粒子系统，由于组合障碍和现有有效的光谱理论方法，它尚未经过深入研究，以分析经典粒子系统。在具有颗粒异质相互作用的复杂系统的背景下，由于棘手的性能，这些技术可能会分解。这项工作为唯一条件下粒子系统的状态空间的拓扑提供了一个工具框，该结果恰好一个粒子一次移动，没有两个粒子可以同时占据相同的顶点。 Johnson $ \ Mathcal {J}（n，k）$图会产生总体结构，我们证明，具有排除属性和单个粒子运动的任何粒子系统都可以嵌入到$ \ Mathcal {J j}（j}（n，k）$的子图中的动力系统。
Understanding the topology of the state space has proven to be extremely efficient for dynamical systems with a continuous state space. On the other hand, for particle systems on finite simple graphs, it has not yet been subject to deep investigation due to combinatorial hurdles and existing efficient spectral theoretic approaches to the analysis of classical particle systems. In the context of complex systems with heterogeneous interactions of particles, these techniques can break down due to intractability. This work provides a tool box of results on the topology of state spaces of particles systems under the sole conditions that exactly one particle moves at a time and no two particles may occupy the same vertex at the same time. The Johnson $\mathcal{J}(n,k)$ graph yields the overarching structure and we prove that any particle system with exclusion property and single particle movements may be embedded as a dynamical system on a sub-graph of $\mathcal{J}(n,k)$.
