A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a rooted edge-labeled tree where each edge is labeled with a single symbol, and the endpoints of the path must be a descendant/ancestor of the other. For a trie with n edges, we show that the number of runs is less than n. We also show an asymptotic lower bound on the maximum density of runs in tries: ${\lim }_{n\to \infty }{\rho }_{\mathcal{T}}(n)/n>0.9932348$ where ${\rho }_{\mathcal{T}}(n)$ is the maximum number of runs in a trie with n edges. Furthermore, we also show an $O(n\log \log n)$ time and $O(n)$ space algorithm for finding all runs.

字符串中的最大重复或运行是最大周期子串，其最小周期最多为子串长度的一半。在本文中，我们考虑对应于树上路径的运行，或者换句话说，在有根边标记的树上，其中每条边都用单个符号标记，并且路径的端点必须是后代/祖先另一个。对于具有n 条边的 trie ，我们表明运行次数小于n。我们还显示了尝试中最大运行密度的渐近下界：${\mathrm{林}}_{n\to \infty }{\rho }_{\mathcal{吨}}(n)/n>0.9932348$ 在哪里 ${\rho }_{\mathcal{吨}}(n)$是具有n 条边的 trie 中的最大运行次数。此外，我们还展示了一个$哦(n\mathrm{日志}\mathrm{日志}n)$ 时间和 $哦(n)$ 用于查找所有运行的空间算法。