Counting genealogical trees (Q1107468)

In the context of the infinitely-many-sites model in population genetics the author considers trees \((x_ 1,...,x_ n)\) of n genes, where the type of each gene \(x_ i\) is given by a sequence \(x_ i=(x_{i0},x_{i1},...)\) of elements in [0,1] representing the sites at which mutations have occurred in the line of descent. The structure of a tree results from the assumptions that every n genes of a tree have a common ancestor and mutations never occur more than once at the same site. The notion of a genealogical tree is introduced by identifying trees which differ only in the order of the n genes or in the labels of the nucleotide sites. Genealogical trees are related to unlabelled graph theoretical trees and recursive solutions for several counting problems have been found.