Abstract A weak order is a way n competitors can rank in an event, where ties are allowed. A weak order can also be thought of as a relation on { 1 , 2 , … , n } that is transitive and complete. We provide the first efficient algorithms to construct universal cycles for weak orders by considering both rank and height representations. Each algorithm constructs the universal cycles in O ( n ) time per symbol using O ( n ) space.

中文翻译：

---

弱阶有效的通用循环构造

摘要 弱排序是 n 个参赛者在一个事件中排名的一种方式，其中允许平局。弱阶也可以被认为是 { 1 , 2 , … , n } 上的一个传递和完备的关系。我们提供了第一个有效的算法，通过考虑秩和高度表示来构建弱阶的通用循环。每个算法使用 O ( n ) 空间在每个符号的 O ( n ) 时间内构造通用循环。