Related papers: Infinite trees
We define the concept of an ultrametric M\"obius space and use this to characterize nonelementary geodesically complete trees.
Discussion of "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481]
Discussion of "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481]
The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to…
In this short note, we find the number of forests of chord diagrams with a given number of trees and a given number of chords.
Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify…
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…
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
In this paper we study the theories of the infinite-branching tree and the $r$-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of…
Discussion of "Treelets--An adaptive multi-Scale basis for sparse unordered data" [arXiv:0707.0481]
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.
We describe the ind- and pro- categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.
The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fr\"uhwirth, we consider an extension of this theory with an additional…
Infinite sequences are considered in the framework of classical logic from a new point of view.
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yield a new formula for the number of NATs. We also obtain…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
The idea of "vertex at the infinity" naturally appears when studying indecomposable injective representations of tree quivers. In this paper we formalize this behavior and find the structure of all the indecomposable injective…
We present a new framework for compositional distributional semantics in which the distributional contexts of lexemes are expressed in terms of anchored packed dependency trees. We show that these structures have the potential to capture…