谱系组合学
Combinatorics of pedigrees
摘要：
一个谱系是一个有向图，其中每个顶点（创始顶点除外）都有两个父节点。本文的主要结果是构造了一个谱系上重构问题的无穷族反例，从而否定地回答了Steel和Hein的一个问题。给出了一些正的重建结果。计数不同（相互非同构）谱系的问题被认为是。已知的下限和上界的谱系数进行了改进，并讨论了它们的相关性，从DNA序列数据的谱系重建。结果表明，信息理论界的分离位点的数量在序列数据中，是最低限度的重建谱系必不可少的将不会显着改变与改进的枚举估计。
英文摘要：
A pedigree is a directed graph in which each vertex (except the founder vertices) has two parents. The main result in this paper is a construction of an infinite family of counter examples to a reconstruction problem on pedigrees, thus negatively answering a question of Steel and Hein. Some positive reconstruction results are also presented. The problem of counting distinct (mutually non-isomorphic) pedigrees is considered. The known lower and upper bounds on the number of pedigrees are improved upon, and their relevance to pedigree reconstruction from DNA sequence data is discussed. It is shown that the information theoretic bound on the number of segregating sites in the sequence data that is minimally essential for reconstructing pedigrees would not significantly change with improved enumerative estimates.
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。
