Related papers: Horton-Strahler numbers for binary butterfly trees…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Binary search trees (BSTs) are fundamental data structures whose performance is largely governed by tree height. We introduce a block model for constructing BSTs by embedding internal BSTs into the nodes of an external BST -- a structure…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We study the distribution of fringe trees in Patricia tries (extending earlier results by Ischebeck (2025)) and compressed binary search trees; both cases are random binary trees that have been compressed by deleting nodes of outdegree 1 so…
Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
A binary tanglegram is a pair <S,T> of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics or software engineering, it is required…
We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposition we obtain a one-to-one…
Recently, Han discovered two formulas involving binary trees which have the interestig property that hooklengths appear as exponents. The purpose of this note is to give a probabilistic proof of one of Han's formulas. Yang has generalized…
We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure…
In this note, by counting some colored plane trees we obtain several binomial identities. These identities can be viewed as specific evaluations of certain generalizations of the Narayana polynomials. As consequences, it provides…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
The hierarchical structure of the butterfly fractal -- the Hofstader butterfly, is found to be described by an octonary tree. In this framework of building the butterfly graph, every iteration generates sextuplets of butterflies, each with…
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree `shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that…
We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
In this paper, we present a new method for determining the optimal pebbling number of a complete binary tree. This method reveals a curious connection between the optimal pebbling numbers of complete binary trees and the Conolly-Fox…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…