芒福德树状图
Mumford dendrograms
摘要：
通过将$p$ -adic数域显式嵌入到Bruhat-Tits树中，提出了一种有效的树图$p$-adic编码.这个域依赖于顶点的子元素的个数，并且是$p$ -进数域的有限扩展。它示出，固定$p$ -进的残余字段的代表允许一个自然的方式编码字符串，通过确定一个给定的字母表与这样的代表。针对$p$-adic数，导出了一个简单的$p$-adic层次分类算法，并将其应用于有限字母表上的字符串. DNA编码的例子提出和讨论。最后，本文给出了$p$ -adic树状图时间序列的新的几何不变量和组合不变量。
英文摘要：
An effective $p$-adic encoding of dendrograms is presented through an explicit embedding into the Bruhat-Tits tree for a $p$-adic number field. This field depends on the number of children of a vertex and is a finite extension of the field of $p$-adic numbers. It is shown that fixing $p$-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet with such representatives. A simple $p$-adic hierarchic classification algorithm is derived for $p$-adic numbers, and is applied to strings over finite alphabets. Examples of DNA coding are presented and discussed. Finally, new geometric and combinatorial invariants of time series of $p$-adic dendrograms are developped.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
