Search results for "combinatoric"
showing 10 items of 1776 documents
Probability and algorithmics: a focus on some recent developments
2017
Jean-François Coeurjolly, Adeline Leclercq-Samson Eds.; International audience; This article presents different recent theoretical results illustrating the interactions between probability and algorithmics. These contributions deal with various topics: cellular automata and calculability, variable length Markov chains and persistent random walks, perfect sampling via coupling from the past. All of them involve discrete dynamics on complex random structures.; Cet article présente différents résultats récents de nature théorique illustrant les interactions entre probabilités et algorithmique. Ces contributions traitent de sujets variés : automates cellulaires et calculabilité, chaînes de Mark…
Coding Partitions
2007
Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD), we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ''unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguous component and other (if any) totally ambiguous components. In the case the code is finite, we give an algorithm for computing its canonical…
Étude de statistiques combinatoires et de leur impact en optimisation évolutionnaire
2021
This thesis studies combinatorial objects, with both an algorithmic and a combinatorial point of view. In the combinatorial part, we take care first, the enumeration of Catalan words avoiding pairs of patterns of length three, presenting the proofs of each case with various enumeration methods. Catalan words are particular growth-restricted words counted by the eponymous integer sequence. More precisely, we systematically explore the structural properties of the sets of words under consideration and give enumerating results by constructive bijections or bivariate generating functions with respect to the length and descent number. Then, we study a sorting machine using two stacks in s…
Equipopularity of descent-equivalent patterns over descent-equivalence classes of words and permutations
2019
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 $\mathcal{D}_n$.
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.
Counting Prefixes of Skew Dyck Paths
2021
We present enumerative results on prefixes of skew Dyck paths by giving recursive relations, Riordan arrays, and generating functions, as well as closed formulas to count the total number of these paths with respect to the length, the height of its endpoint and the number of left steps.