Related papers: A One-to-One Correspondence between Natural Number…
Let $T$ be a rooted tree, and $V(T)$ its set of vertices. A subset $X$ of $V(T)$ is called an infima closed set of $T$ if for any two vertices $u,v\in X$, the first common ancestor of $u$ and $v$ is also in $X$. This paper determines the…
A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and…
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete binary trees whose leaves are labeled by letters of an…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
The derivation trees of a tree adjoining grammar provide a first insight into the sentence semantics, and are thus prime targets for generation systems. We define a formalism, feature-based regular tree grammars, and a translation from…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
Rotation distance between rooted binary trees is the minimum number of simple rotations needed to transform one tree into the other. Computing the rotation distance between a pair of rooted trees can be quickly reduced in cases where there…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of…
Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{\'e}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary…
In this study, we explore a novel approach to demonstrate the countability of rational numbers and illustrate the relationship between the Calkin-Wilf tree and the Stern-Brocot tree in a more intuitive manner. By employing a growth pattern…
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological tree'. In this work, we are interested in the continuum…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
Ranked tree-child networks are a recently introduced class of rooted phylogenetic networks in which the evolutionary events represented by the network are ordered so as to respect the flow of time. This class includes the well-studied…
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Let $T$ be a tree, we show that the null space of the adjacency matrix of $T$ has relevant information about the structure of $T$. We introduce the Null Decomposition of trees, and use it in order to get formulas for independence number and…
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…
Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…