Related papers: Approximate Fixed Point Property for Digital Trees…

For $d\ge 2$ and an odd prime power $q$, consider the vector space $\mathbb{F}_q^d$ over the finite field $\mathbb{F}_q$, where the distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined as $\sum_{i=1}^d…

Building upon work of L\"{u}cke and Schlicht, we study (higher) Kurepa trees through the lens of higher descriptive set theory, focusing in particular on various perfect set properties and representations of sets of branches through trees…

The paper is devoted to a study of certain fixed point properties, and their relatives, in the context of full automorphism groups of countable rooted trees. Namely, we study Serre's property (FA'), also called unsplittability, property…

In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined \,$(\,\epsilon \,,\, \lambda\,)$\,…

This paper is concerned with the fast computation of a relation $\R$ on the edge set of connected graphs that plays a decisive role in the recognition of approximate Cartesian products, the weak reconstruction of Cartesian products, and the…

It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for…

In this paper we investigate the geometric properties of quasi-trees, and prove some equivalent criteria. We give a general construction of a tree that approximates the ends of a geodesic space, and use this to prove that every quasi-tree…

A compact polyhedron $X$ is said to have the Bounded Index Property for Homotopy Equivalence (BIPHE) if there is a finite bound $\mathcal{B}$ such that for any homotopy equivalence $f:X\rightarrow X$ and any fixed point class $\mathbf{F}$…

Let $p$ be an odd prime and $A \subseteq \mathbb{F}_p$ be a subset of the finite field with $p$ elements. We show that $A \times A \subseteq \mathbb{F}_p^2$ determines at least a constant multiple of $\min\{p, |A|^{3/2}\}$ distinct pinned…

The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

Probabilistic relational models such as parametric factor graphs enable efficient (lifted) inference by exploiting the indistinguishability of objects. In lifted inference, a representative of indistinguishable objects is used for…

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…

We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…

In this technical note, we derive a closed-form expression for the affine transformation mapping local image patches between two calibrated views. We show that the transformation is a function of the relative camera pose, the image…

We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various…

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally…

A locally compact groupoid is said to be exact if its associated reduced crossed product functor is exact. In this paper, we establish some permanence properties of exactness, including generalizations of some known results for exact…

We give an axiomatic characterization of the fixed point index of an $n$-valued map. For $n$-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting…

We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…