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Graphes, Théorie des --- Graph theory. --- Graphes orientés. --- Directed graphs --- Algebres de boole --- Ensembles flous

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Ce livre est une introduction d velopp e la th orie des graphes. Autour de cette th orie se d veloppe aujourd'hui l'un des domaines les plus f conds et les plus dynamiques des mah matiques et de l'informatique. La th orie des graphes permet de r pr senter un ensemble complexe d'objets en exprimant les relations entre les l ments: r seaux de communication, circuits lectriques, etc. Le livre pr sente le langage et les notions l mentaires de cette th orie, les diff rents types de graphes (bipartis, arbres, arborescences, graphes eul riens et hamiltoniens, etc.); il tudie les relations entre les g

Computer Science --- Engineering mathematics --- Computational complexity. --- Graph theory. --- Isomorphisms (Mathematics). --- Mathematics. --- Engineering & Applied Sciences --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Foundations --- Extremal problems

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Quantitative methods in social research --- Sociology --- Research --- Tables --- Statistics --- Graphic methods --- Sociologie --- Méthodes graphiques --- Recherche --- -Graphic methods --- Graphics --- Graphs --- Geometrical drawing --- Least squares --- Mathematics --- Mechanical drawing --- Social theory --- Social sciences --- Graphic methods. --- Research. --- Méthodes graphiques --- Sociological research --- Sociology - Research --- Methodologie

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In this master's thesis, we explore the notion of growth of groups. For any finitely generated group, one can define a growth function associated to a fixed finite set of generators. It is the mapping of any positive integer n to the number of elements of a group that can be written in n generators. This allows for a classification of groups according to their growth, examples of such classes are groups of polynomial growth and groups of exponential growth. In the thesis, we define this concept with the necessary rigor. We then proceed to prove that groups of polynomial growth and virtually nilpotent groups are the same (Gromov's theorem). We also provide an example of a group, the Grigorchuk group, that has neither polynomial nor exponential growth. Dans ce mémoire, on développe la notion de croissance des groupes. Pour tout groupe finiment engendré, on définit la fonction de croissance associée à un système de générateurs finis fixé. C'est la fonction qui à un naturel n associe le nombre d'éléments du groupe qui peuvent être écrits en n générateurs. Une classification des groupes selon leur croissance est possible. On définit par exemple les groupes à croissance polynomiale ou à croissance exponentielle. Dans le mémoire, on définit ce concept avec la rigueur nécessaire. Ensuite, on prouve que les groupes virtuellement nilpotents sont à croissance polynomiale et réciproquement (théorème de Gromov). On donnera également de groupe, le groupe de Grigorchuk, qui n'est ni à croissance polynomiale ni à croissance exponentielle.

Théorie des groupes --- Théorie géométrique des groupes --- Théorème de Gromov --- Croissance des groupes --- Groupe de Grigorchuk --- Groupes nilpotents --- Graphes de Cayley --- Quasi-isométries --- Quasi-isometries --- Group theory --- Geometric group theory --- Gromov's theorem --- Growth of groups --- Grigorchuk group --- Nilpotent groups --- Cayley graphs --- Physique, chimie, mathématiques & sciences de la terre > Mathématiques

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Electronic data processing --- Database management --- Data structures (Computer science) --- Database management. --- 681.3*D22 --- 681.3*E1 --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Tools and techniques: decision tables; flow charts; modules and interfaces; programmer workbench; software libraries; structured programming; top-down programming; user interfaces (Software engineering) --- Data structures: arrays; graphs; lists; tables; trees --- Automation --- 681.3*E1 Data structures: arrays; graphs; lists; tables; trees --- 681.3*D22 Tools and techniques: decision tables; flow charts; modules and interfaces; programmer workbench; software libraries; structured programming; top-down programming; user interfaces (Software engineering) --- Systèmes, Conception de --- System design --- Gestion --- Management --- Informatique --- Systèmes, Conception de --- System design. --- Fichiers (informatique) --- Organisation