Related papers: About Fibonacci trees. I
This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. Two auxiliary…
In analogy to a concept of Fibonacci trees, we define the leaf-Fibonacci tree of size $n$ and investigate its number of nonisomorphic leaf-induced subtrees. Denote by $f_0$ the one vertex tree and $f_1$ the tree that consists of a root with…
We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…
A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number…
We show that the structure of a growing tree preserves an information on the shape of an initial graph. For the exponential trees, evidence of this kind of memory is provided by means of the iterative equations, derived for the moments of…
We study the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number 1. We define the tree recursively in the following way: if…
The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of…
We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the colors of a parent vertex and its child. This…
In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative integers to be realized as a rooted tree.
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one can associate a tree in a natural way. It is known that the corresponding Poincare series P(X) = \sum_i N_i X^i is rational, where N_i is the number of nodes of the…
We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…
Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic…
In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…
A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on `2-SAT') that efficiently determines…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…