Search results for "Combinatorics"
showing 10 items of 1770 documents
Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
2018
Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .
L'accès à la titularisation des non reçus au concours de l'enseignement : L'impact du premier emploi sur le positionnement dans la file d'attente
2016
This research, as a part of a PhD thesis in educational sciences relates to the social network and the transversal skills developed by the Bachelor's degree students ("Licence") in a French college. Overall, this work aims at identifying and estimating origins and effects of student social integration and transversal skills within the college careers. Four areas of student social integration and ten skills stemming from a reference table are measured by an original questionnaire. In this paper, the first preliminary results of this work are presented and reveal the influence of various personal and contextual factors on the integration and skills scores stated by students.
Suffix array and Lyndon factorization of a text
2014
Abstract The main goal of this paper is to highlight the relationship between the suffix array of a text and its Lyndon factorization. It is proved in [15] that one can obtain the Lyndon factorization of a text from its suffix array. Conversely, here we show a new method for constructing the suffix array of a text that takes advantage of its Lyndon factorization. The surprising consequence of our results is that, in order to construct the suffix array, the local suffixes inside each Lyndon factor can be separately processed, allowing different implementative scenarios, such as online, external and internal memory, or parallel implementations. Based on our results, the algorithm that we prop…
Composition operators on the Schwartz space
2018
[EN] We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.
Special factors and the combinatorics of suffix and factor automata
2011
AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.
Grover’s Search with Faults on Some Marked Elements
2016
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size N using $$O\sqrt{N}$$ queries. It provides a significant speed-up over any classical algorithm [2]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [1, 4]. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in $$O\sqrt{N}$$ queries.
Radio k-Labelings for Cartesian Products of Graphs
2005
International audience; Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that |f(x)−f(y)| ≥ k+1−dG(x,y), for any two vertices x and y, where dG(x,y) is the distance between x and y in G. The radio k-chromatic number is the minimum of max{f(x)−f(y):x,y ∈ V(G)} over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian pro…
A branch-and-cut algorithm for the soft-clustered vehicle-routing problem
2021
Abstract The soft-clustered vehicle-routing problem is a variant of the classical capacitated vehicle-routing problem (CVRP) in which customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. We introduce a novel symmetric formulation of the problem in which the clustering part is modeled with an asymmetric sub-model. We solve the new model with a branch-and-cut algorithm exploiting some known valid inequalities for the CVRP that can be adapted. In addition, we derive problem-specific cutting planes and new heuristic and exact separation procedures. For square grid instances in the Euclidean plane, we provide lower-bounding techniques …
Stable maps from surfaces to the plane with prescribed branching data
2007
Abstract We consider the problem of constructing stable maps from surfaces to the plane with branch set a given set of curves immersed (except possibly with cusps) in the plane. Various constructions are used (1) piecing together regions immersed in the plane (2) modifying an existing stable map by a sequence of codimension one transitions (swallowtails etc) or by surgeries. In (1) the way the regions are pieced together is described by a bipartite graph (an edge C* corresponds to a branch curve C with the vertices of C* corresponding to the two regions containing C). We show that any bipartite graph may be realized by a stable map and we consider the question of realizing graphs by fold ma…
The Shuffle Product: New Research Directions
2015
In this paper we survey some recent researches concerning the shuffle operation that arise both in Formal Languages and in Combinatorics on Words.