Related papers: On embedded trees and lattice paths

This paper considers the enumeration of ternary trees (i.e. rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree…

We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…

Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…

We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…

Various lattice path models are reviewed. The enumeration is done using generating functions. A few bijective considerations are woven in as well. The kernel method is often used. Computer algebra was an essential tool. Some results are…

Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…

Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially…

This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our…

We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary…

In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…

We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained…

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…

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…

Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…

For a labeled tree on the vertex set $\set{1,2,\ldots,n}$, the local direction of each edge $(i\,j)$ is from $i$ to $j$ if $i<j$. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges…

A subtree can be induced in a natural way by a subset of leaves of a rooted tree. We study the number of nonisomorphic such subtrees induced by leaves (leaf-induced subtrees) of a rooted tree with no vertex of outdegree 1 (topological…

We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face of degree d. We develop two approaches in parallel: the…

In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a…

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting…