Related papers: Intervals of balanced binary trees in the Tamari l…

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. A particular focus of research has been the…

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological…

We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some…

In this paper, we explain how the Tamari lattice arises in the context of the representation theory of quivers, as the poset whose elements are the torsion classes of a directed path quiver, with the order relation given by inclusion.

Given a bounded valence, bushy tree T, we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T'. This theorem has many applications: quasi-isometric rigidity…

A balanced pair in a finite ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of linear extensions of $P$ that put $x$ before $y$ is in the real interval $[1/3, 2/3]$. We prove that every finite $N$-free…

Hex-trees are identified as a particular instance of weighted unary-binary trees. The Horton-Strahler numbers of these objects are revisited, and, thanks to a substitution that is not immediately intuitive, explicit results are possible.…

This thesis comes within the scope of algebraic combinatorics and studies problems related to three orders on permutations: the two said weak orders (right and left) and the strong order or Bruhat order. The first part deals with bases of…

For classical discrete systems under constant composition, we re-examine how linear-nonlinear boundary in canonical ensemble, connecting a set of potential energy surface and that of microscopic configuration in thermodynamic equilibrium,…

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 conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give…

This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations. A polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed. This problem…

This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…

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…

We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…

Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly…

In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators…

Tree balance plays an important role in phylogenetics and other research areas, which is why several indices to measure tree balance have been introduced over the years. Nevertheless, a formal definition of what a balance index actually is…