Related papers: The Fixed Point Property for Posets of Small Width
The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs…
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
There are many results showing the connection and phenomenon between some low-dimensional manifolds with the profinite completions of their fundamental groups. We focus on some Seifert 4-manifolds about the extent of their profinite…
We study the problems of bounding the number weak and strong independent sets in $r$-uniform, $d$-regular, $n$-vertex linear hypergraphs with no cross-edges. In the case of weak independent sets, we provide an upper bound that is tight up…
We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…
In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main…
We explore the enumeration of some natural classes of graded posets, including all graded posets, (2+2)- and (3+1)-avoiding graded posets, (2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain enumerative and structural…
In this survey we present a generalization of the notion of metric space and some applications to discrete structures as graphs, ordered sets and transition systems. Results in that direction started in the middle eighties based on the…
Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in…
We investigate the $O(N)$--symmetric $\phi^6$ theory in three spacetime dimensions using dimensional regularisation and minimal subtraction. The predictions of other methods are scrutinised in a large-$N$ expansion. We show how the…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an…
Let $(P,\leq)$ be a finite poset (partially ordered set), where $P$ has cardinality $n$. Consider linear extensions of $P$ as permutations $x_1x_2\cdots x_n$ in one-line notation. For distinct elements $x,y\in P$, we define…
Let $(X,\le)$ be a {\em non-empty strictly inductive poset}, that is, a non-empty partially ordered set such that every non-empty chain $Y$ has a least upper bound lub$(Y)\in X$, a chain being a subset of $X$ totally ordered by $\le$. We…
Properties of intervals in the lattice of antichains of subsets of a universe of finite size are investigated. New objects and quantities in this lattice are defined. Expressions and numerical values are deduced for the number of connected…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
The cross--product conjecture (CPC) of Brightwell, Felsner and Trotter (1995) is a two-parameter quadratic inequality for the number of linear extensions of a poset $P= (X, \prec)$ with given value differences on three distinct elements in…
I study the two-dimensional defects of the $d$ dimensional critical $O(N)$ model and the defect RG flows between them. By combining the $\epsilon$-expansion around $d = 4$ and $d = 6$ as well as large $N$ techniques, I find new conformal…
In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contraction mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also,…
We give necessary and sufficient conditions for a nonexpansive map on a finite dimensional normed space to have a nonempty, bounded set of fixed points. Among other results we show that if $f : V \rightarrow V$ is a nonexpansive map on a…