9 papers
Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections
Michael Fuchs, Bernhard Gittenberger, Marefatollah Mansouri
In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with reticulation vertices and explicit exponential generating functions…
Protection numbers in simply generated trees and Pólya trees
Bernhard Gittenberger, Zbigniew Gołębiewski, Isabella Larcher +1
We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in Pólya trees, and in unlabelled non-plane binary tre…
Distribution of variables in lambda-terms with restrictions on De Bruijn indices and De Bruijn levels
Bernhard Gittenberger, Isabella Larcher
We investigate the number of variables in two special subclasses of lambda-terms that are restricted by a bound of the number of abstractions between a variable and its binding lam…
On the Number of Increasing Trees with Label Repetitions
Olivier Bodini, Antoine Genitrini, Bernhard Gittenberger +1
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and t…
Threshold functions for small subgraphs in simple graphs and multigraphs
Gwendal Collet, Élie de Panafieu, Danièle Gardy +2
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce th…
Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks
Michael Fuchs, Bernhard Gittenberger, Marefatollah Mansouri
In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely op…