论文标题
霍顿·斯特拉勒（Horton-Strahler
The Horton-Strahler Number of Conditioned Galton-Watson Trees
论文作者
论文摘要
一棵树的霍顿 - 斯特拉勒数量是其分支复杂性的量度。在文献中也被称为寄存器函数。我们表明，对于具有有限差异的关键Galton-Watson树，条件为$ n $，Horton-Strahler编号在概率上以$ \ frac {1} {2} {2} {2} {2} \ log_2 n $的概率生长。我们进一步定义了此数字的一些概括。其中包括刚性霍顿·斯特拉勒（Horton-Strahler）编号和$ k $ aright的寄存器功能，我们证明了类似于标准案例的渐近结果。
The Horton-Strahler number of a tree is a measure of its branching complexity; it is also known in the literature as the register function. We show that for critical Galton-Watson trees with finite variance conditioned to be of size $n$, the Horton-Strahler number grows as $\frac{1}{2}\log_2 n$ in probability. We further define some generalizations of this number. Among these are the rigid Horton-Strahler number and the $k$-ary register function, for which we prove asymptotic results analogous to the standard case.
