Related papers: Finite trees are Ramsey under topological embeddin…
We prove that for any choice of parameters $k,t,\lambda$ the class of all finite ordered designs with parameters $k,t,\lambda$ is a Ramsey class.
Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. In this paper we propose a new strategy to show that a class…
We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation.…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
This paper investigates big Ramsey degrees of unrestricted relational structures in (possibly) infinite languages. Despite significant progress in the study of big Ramsey degrees, the big Ramsey degrees of many classes of structures with…
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths. These results show a strong link between the properties of these graph classes considered from the point…
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…
This paper proves that two differently defined rooted binary trees are isomorphic. The first tree is one associated to a version of Farey sequences where the vertices correspond to the open intervals formed by two successive terms in the…
We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and…
Each labeled rooted tree is associated with a hyperplane arrangement, which is free with exponents given by the depths of the vertices of this tree. The intersection lattices of these arrangements are described through posets of forests.…
A characterization of finite homogeneous ultrametric spaces and finite ultrametric spaces generated by unrooted labeled trees is found in terms of representing trees. A characterization of finite ultrametric spaces having perfect strictly…
Parabolic (resp. hyperbolic) self-embeddings of trees are those which do not fix a non-empty finite subtree and preserve precisely one (resp. two) end(s). We prove that a locally finite tree having a parabolic self-embedding is mutually…
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.
This paper is devoted to proving an infinite sequence of relations for rooted tree maps. On the way, we also give a basis for the space of rooted tree maps.
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…
\emph{A root frame} for $\mathbb{R}^d$ is a finite frame whose vectors form a root system. In this note we establish some elementary properties of this class of frames and prove that root frames constitute a subclass of scalable frames. In…
Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
The purpose is to study the strength of Ramsey's Theorem for pairs restricted to recursive assignments of $k$-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number $k \geq 2$, Ramsey's…
We construct a tree T of maximal degree 3 with infinitely many leaves such that whenever finitely many of them are removed, the remaining tree is isomorphic to T. In this sense T resembles an infinite star.