Related papers: Sumsets and fixed points of substitutions

The purpose of this work is to introduce a general class of $C_G$-simulation functions and obtained some new coincidence and common fixed points results in metric spaces. Some useful examples are presented to illustrate our theorems.…

Let $A, B\subseteq \mathbb{Z}$ be finite, nonempty subsets with $\min A=\min B=0$, and let $$\delta(A,B)={\begin{array}{ll} 1 & \hbox{if} A\subseteq B, 0 & \hbox{otherwise.} If $\max B\leq \max A\leq |A|+|B|-3$ and \label{one}|A+B|\leq…

For an interval [1,N] in the natural numbers, investigating subsets S of [1,N] such that |{(x,y) in S^2:x+y in S}|=0, known as sum-free sets, has attracted considerable attention. In this paper, we define r(S):=|{(x,y) in S^2: x+y in S}|…

Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…

We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if $t$ is an integer different from $0, 1$ or -1 and if $\A \subset \Zp$ is not too large (with respect to $p$),…

Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…

Let $A \subset \mathbb R$ and $G \subset A \times A$. We prove that, for any $\lambda \in \mathbb R \setminus \{-1,0,1\}$, \[ \max \{|A+_G A|, |A+_G \lambda A|, |A\cdot_G A|\} \gg |G|^{6/11}. \]

Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ are infinite. Our proof…

We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…

We introduce dependent adders. A dependent adder $A$ has for every $x \in A$ a way of adding together $x$ many elements of $A$. We provide examples from many disparate branches of mathematics. Examples include the field with one element…

Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…

One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the…

In this paper, we study the "sum composition problem" between two lists $A$ and $B$ of positive integers. We start by saying that $B$ is "sum composition" of $A$ when there exists an ordered $m$-partition $[A_1,\ldots,A_m]$ of $A$ where $m$…

The \emph{sum-product phenomenon} predicts that a finite set $A$ in a ring $R$ should have either a large sumset $A+A$ or large product set $A \cdot A$ unless it is in some sense "close" to a finite subring of $R$. This phenomenon has been…

For a positive integer $n$, let $\mZ$ be the set of all non-negative integers modulo $n$ and $\sP(\mZ)$ be its power set. A modular sumset valuation or a modular sumset labeling of a given graph $G$ is an injective function $f:V(G) \to…

For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…

Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…

This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…

For finite sets A and B in the plane, we write A+B to denote the set of sums of the elements of A and B. In addition, we write tr(A) to denote the common number of triangles in any triangulation of the convex hull of A using the points of A…