We prove that among all flag homology 5-manifolds with n vertices, the join of 3 circles of as equal length as possible is the unique maximizer of all the face numbers. The same upper bounds on the face numbers hold for 5-dimensional flag Eulerian normal pseudomanifolds.

中文翻译：

---

标记同源性5流形的上限定理

我们证明，在具有n个顶点的所有标志同源性5流形中，尽可能长的3个圆的连接是所有面数的唯一最大化。面部编号的相同上限适用于5维标志Eulerian正常伪流形。