Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of ancestral configurations for matching gene trees and
  species trees   Given a gene tree and a species tree, ancestral configurations represent the
combinatorially distinct sets of gene lineages that can reach a given node of
the species tree. They have been introduced as a data structure for use in the
recursive computation of the conditional probability under the multispecies
coalescent model of a gene tree topology given a species tree, the cost of this
computation being affected by the number of ancestral configurations of the
gene tree in the species tree. For matching gene trees and species trees, we
obtain enumerative results on ancestral configurations. We study ancestral
configurations in balanced and unbalanced families of trees determined by a
given seed tree, showing that for seed trees with more than one taxon, the
number of ancestral configurations increases for both families exponentially in
the number of taxa $n$. For fixed $n$, the maximal number of ancestral
configurations tabulated at the species tree root node and the largest number
of labeled histories possible for a labeled topology occur for trees with
precisely the same unlabeled shape. For ancestral configurations at the root,
the maximum increases with $k_0^n$, where $k_0 \approx 1.5028$ is a quadratic
recurrence constant. Under a uniform distribution over the set of labeled trees
of given size, the mean number of root ancestral configurations grows with
$\sqrt{3/2}(4/3)^n$ and the variance with approximately $1.4048(1.8215)^n$. The
results provide a contribution to the combinatorial study of gene trees and
species trees.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
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The categories of this paper are: cs
18
The categories of this paper are: econ