标题： 任意长度非二元字母表上的未聚类BWT 显示英文标题

标题： Unclustered BWTs of any Length over Non-Binary Alphabets

摘要： 我们证明，对于每个整数$n > 0$和每个大小为$k \geq 3$的字母表$\Sigma_k$，存在一个长度为$n$的项链，其 Burrows-Wheeler 变换（BWT）是完全不聚类的，即它恰好包含$n$个运行，且没有两个连续的相同符号。这些词代表了 BWT 在聚类方面的最坏情况行为，因为 BWT 运行的数量是最大的。我们还建立了它们数量的一个下界。这与二进制情况形成对比，其中完全不聚类的 BWT 的存在仍然是一个开放问题，与 Artin 关于原根的猜想有关。 显示英文摘要

摘要： We prove that for every integer $n > 0$ and for every alphabet $\Sigma_k$ of size $k \geq 3$, there exists a necklace of length $n$ whose Burrows-Wheeler Transform (BWT) is completely unclustered, i.e., it consists of exactly $n$ runs with no two consecutive equal symbols. These words represent the worst-case behavior of the BWT for clustering, since the number of BWT runs is maximized. We also establish a lower bound on their number. This contrasts with the binary case, where the existence of infinitely many completely unclustered BWTs is still an open problem, related to Artin's conjecture on primitive roots.