论文标题
中间生长树的分支数量
The branching number of intermediate growth trees
论文作者
论文摘要
我们介绍了一个“中间分支机构”（IBN），该数字捕获了中间生长树的分支，精神与精心研究的分支数量相似。我们表明，IBN是树上几个随机过程的关键阈值，并在某些感兴趣的例子上分析IBN。我们的主要结果是一种算法，可以在某些排列的花圈产品中找到带有大IBN的球形对称树。我们通过使用这些树木在某些内中间生长组上为消防员问题获得第一个紧密界限，证明了这些树对中间生长组的有用性。
We introduce an "intermediate branching number"(IBN) which captures the branching of intermediate growth trees, similar in spirit to the well-studied branching number of exponential growth trees. We show that the IBN is the critical threshold for several random processes on trees, and analyze the IBN on some examples of interest. Our main result is an algorithm to find spherically symmetric trees with large IBN inside some permutation wreath products. We demonstrate the usefulness of these trees to the study of intermediate growth groups by using them to get the first tight bounds for the firefighter problem on some inetrmediate growth groups.
