Search results for " Combinatoric"
showing 10 items of 299 documents
Equivalence classes of Dyck paths modulo some statistics
2015
International audience; We investigate new equivalence relations on the set $\mathcal{D}_n$ of Dyck paths relatively to the three statistics of double rises, peaks and valleys. Two Dyck paths ar $r$-equivalent (resp. $p$-equivalent and $v$-equivalent) whenever the positions of their double rises (res. peaks and valleys) are the same. Then, we provide generating functions for the numbers of $r$-, $p$- and $v$-equivalence classes of $\mathcal{D}_n$.
On List Coloring with Separation of the Complete Graph and Set System Intersections
2022
We consider the following list coloring with separation problem: Given a graph $G$ and integers $a,b$, find the largest integer $c$ such that for any list assignment $L$ of $G$ with $|L(v)|= a$ for any vertex $v$ and $|L(u)\cap L(v)|\le c$ for any edge $uv$ of $G$, there exists an assignment $\varphi$ of sets of integers to the vertices of $G$ such that $\varphi(u)\subset L(u)$ and $|\varphi(v)|=b$ for any vertex $u$ and $\varphi(u)\cap \varphi(v)=\emptyset$ for any edge $uv$. Such a value of $c$ is called the separation number of $(G,a,b)$. Using a special partition of a set of lists for which we obtain an improved version of Poincar\'e's crible, we determine the separation number of the c…
Asymptotic bit frequency in Fibonacci words
2021
It is known that binary words containing no $k$ consecutive 1s are enumerated by $k$-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length $n$ having this property.
On the tensor degree of finite groups
2013
We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.
Optimal recovery of a radiating source with multiple frequencies along one line
2020
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
The b-chromatic number of power graphs
2003
The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.
A simulation function approach for best proximity point and variational inequality problems
2017
We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
Statistical properties of general Markov dynamical sources: applications to information theory
2004
In \textitDynamical sources in information theory: fundamental intervals and word prefixes, B. Vallée studies statistical properties of words generated by dynamical sources. This is done using generalized Ruelle operators. The aim of this article is to generalize sources for which the results hold. First, we avoid the use of Grotendieck theory and Fredholm determinants, this allows dynamical sources that cannot be extended to a complex disk or that are not analytic. Second, we consider Markov sources: the language generated by the source over an alphabet \textbfM is not necessarily \textbfM^*.
Models of the population playing the Rock-Paper-Scissors game
2018
We consider discrete dynamical systems coming from the models of evolution of populations playing rock - paper - scissors game . Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.
On modified α-ϕ-fuzzy contractive mappings and an application to integral equations
2016
Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.