Search results for "DISCRETE"
showing 10 items of 2205 documents
Equivalence classes of permutations modulo excedances
2014
International audience
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.
Fibonacci q-decreasing words: enumerative results and Gray codes
2022
Gray code for permutations with a fixed number of left-to-right minima
2013
International audience
Q-bonacci words and numbers
2022
We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational $q$, we enumerate binary words of length $n$ whose maximal factors of the form $0^a1^b$ satisfy $a = 0$ or $aq > b$. When $q$ is an integer we rediscover classical multi-step Fibonacci numbers: Fibonacci, Tribonacci, Tetranacci, etc. When $q$ is not an integer, obtained recurrence relations are connected to certain restricted integer compositions. We also discuss Gray codes for these words, and a possibly novel generalization of the golden ratio.
Packing coloring and subsets preserving path distance
2016
International audience
Pattern avoiding permutations modulo pure descent
2017
International audience
Qubonacci words
2021
International audience
Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications
2013
The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.