We prove that, for a finite ordered set P that contains no crowns with 6 or more elements, it can be determined in polynomial time if P has the fixed point property. This result is obtained by proving that every such ordered set must contain a point of rank 1 that has a unique lower cover or a retractable minimal element.

中文翻译：

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不包含具有 6 个或更多元素的冠的有限有序集的不动点属性

我们证明，对于一个不包含6个或更多元素冠的有限有序集P，如果P具有不动点性质，则可以在多项式时间内确定。这个结果是通过证明每个这样的有序集合必须包含一个秩为 1 的点来获得的，该点具有唯一的下覆盖或可伸缩的最小元素。