SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 636-670, January 2021.
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an intersection of the partition lattice of $n$ elements and a lattice of invariant subspaces of the associated adjacency matrix. We assign integer tuples with synchrony subspaces and use them for identifying equivalent synchrony subspaces to be merged. Based on this equivalence, the initial lattice of synchrony subspaces can be reduced to a lattice of synchrony subspaces which corresponds to a simple eigenvalue case discussed in our previous work. The result is a reduced lattice of synchrony subspaces, which affords a well-defined nonnegative integer index that leads to bifurcation analysis in regular coupled cell networks.

中文翻译：

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同步子空间的缩格及其索引

SIAM应用动力系统杂志，第20卷，第2期，第636-670页，2021年1月。
对于常规耦合小区网络，同步子空间是在网络邻接矩阵下不变的多对角子空间。一个$ n $元正则网络的同步子空间的完整格子可以看作是$ n $个元素的分隔格子和相关联的邻接矩阵的不变子空间的格子的交集。我们为整数元组分配同步子空间，并将其用于标识要合并的等效同步子空间。基于此等价关系，可以将同步子空间的初始晶格简化为同步子空间的晶格，这与我们先前工作中讨论的简单特征值情况相对应。结果是减少了同步子空间的晶格，