Academic literature on the topic 'Combinatoire géométrique'
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Journal articles on the topic "Combinatoire géométrique":
Ferenczi, Sébastien. "Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$." Bulletin de la Société mathématique de France 123, no. 2 (1995): 271–92. http://dx.doi.org/10.24033/bsmf.2260.
Le Roux, Brigitte. "Inférence combinatoire en analyse géométrique des données." Mathématiques et sciences humaines, no. 144 (December 1, 1998). http://dx.doi.org/10.4000/msh.2781.
Ceballos, Cesar, Jean-Philippe Labbé, and Christian Stump. "Multi-cluster complexes." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AR,..., Proceedings (January 1, 2012). http://dx.doi.org/10.46298/dmtcs.3014.
Aguiar, Marcelo, and Kile T. Petersen. "The module of affine descents." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (January 1, 2013). http://dx.doi.org/10.46298/dmtcs.12811.
Beazley, Elizabeth T. "Maximal Newton polygons via the quantum Bruhat graph." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AR,..., Proceedings (January 1, 2012). http://dx.doi.org/10.46298/dmtcs.3092.
Jones, Brant. "Deodhar Elements in Kazhdan-Lusztig Theory." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AJ,..., Proceedings (January 1, 2008). http://dx.doi.org/10.46298/dmtcs.3645.
Bürgisser, Peter, and Christian Ikenmeyer. "A max-flow algorithm for positivity of Littlewood-Richardson coefficients." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (January 1, 2009). http://dx.doi.org/10.46298/dmtcs.2749.
Iriarte Giraldo, Benjamin. "Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (January 1, 2011). http://dx.doi.org/10.46298/dmtcs.2918.
Colmenarejo, Laura. "Stability properties of Plethysm: new approach with combinatorial proofs (Extended abstract)." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (January 1, 2015). http://dx.doi.org/10.46298/dmtcs.2526.
Lenz, Matthias. "Hierarchical Zonotopal Power Ideals." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (January 1, 2011). http://dx.doi.org/10.46298/dmtcs.2939.
Dissertations / Theses on the topic "Combinatoire géométrique":
Sage, Marc. "Combinatoire algébrique et géométrique des nombres de Hurwitz." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00804228.
Siegel, Anne. "Représentations géométrique, combinatoire et arithmétique des systèmes subsitutifs de type Pisot." Aix-Marseille 2, 2000. http://www.theses.fr/2000AIX22075.
Skapin, Xavier. "Utilisation du produit cartésien en modélisation géométrique 4D pour l'animation." Poitiers, 2001. http://www.theses.fr/2001POIT2301.
We work in the scope of 4D (space-time) modelling for animation. Extending 3D modelling methods to dimension 4 is the main advantage of 4D modelling, but interpreting a 4D object as an animation and controlling the construction of this object are the main drawbacks of 4D modelling. Our method uses space-time objects of dimension lesser than 4 as operands of the cartesian product operation to create an object of greater dimension, whose interpretation is deduced from operands'. We made a case study about cartesian product of basic operands defined as point trajectories. This study led to a method for interpreting and controlling 4D objects resulting from cartesian product. We have created a topologically-based 4D geometrical modeler, allowing us to design elaborate animations. We have adapted cartesian product operation to semi-simplicial sets, generalized maps, n-maps and closed chains of maps. Each of these definitions corresponds to an algorithm with an optimal complexity in time
Ledent, Jérémy. "Sémantique géométrique pour la calculabilité asynchrone." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX099/document.
The field of fault-tolerant protocols studies which concurrent tasks are solvable in various computational models where processes may crash. To answer these questions, powerful mathematical tools based on combinatorial topology have been developed since the 1990’s. In this approach, the task that we want to solve, and the protocol that we use to solve it, are both modeled using chromatic simplicial complexes. By definition, a protocol solves a task when there exists a particular simplicial map between those complexes.In this thesis we study these geometric methods from the point of view of semantics. Our first goal is to ground this abstract definition of task solvability on a more concrete one, based on interleavings of execution traces. We investigate various notions of specification for concurrent objects, in order to define a general setting for solving concurrent tasks using shared objects. We then show how the topological definition of task solvability can be derived from it.In the second part of the thesis, we show that chromatic simplicial complexes can actually be used to interpret epistemic logic formulas. This allows us to understand the topological proofs of task unsolvability in terms of the amount of knowledge that the processes should acquire in order to solve a task.Finally, we present a few preliminary links with the directed space semantics for concurrent programs. We show how chromatic subdivisions of a simplex can be recovered by considering combinatorial notions of directed paths
Philippe, Eva. "Geometric realizations using regular subdivisions : construction of many polytopes, sweep polytopes, s-permutahedra." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS079.
This thesis concerns three problems of geometric realizations of combinatorial structures via polytopes and polyhedral subdivisions. A polytope is the convex hull of a finite set of points in a Euclidean space R^d. It is endowed with a combinatorial structure coming from its faces. A subdivision is a collection of polytopes whose faces intersect properly and such that their union is convex. It is regular if it can be obtained by taking the lower faces of a lifting of its vertices in one dimension higher.We first present a new geometric construction of many combinatorially different polytopes of fixed dimension and number of vertices. This construction relies on showing that certain polytopes admit many regular triangulations. It allows us to improve the best known lower bound on the number of combinatorial types of polytopes.We then study the projections of permutahedra, that we call sweep polytopes because they model the possible orderings of a fixed point configuration by hyperplanes that sweep the space in a constant direction. We also introduce and study a combinatorial abstraction of these structures: the sweep oriented matroids, that generalize Goodman and Pollack's theory of allowable sequences to dimensions higher than 2.Finally, we provide geometric realizations of the s-weak order, a combinatorial structure that generalizes the weak order on permutations, parameterized by a vector s with positive integer coordinates. In particular, we answer Ceballos and Pons conjecture that the s-weak order can be realized as the edge-graph of a polytopal complex that is moreover a subdivision of a permutahedron
Diakité, Abdoulaye Abou. "Application des cartes combinatoires à la modélisation géométrique et sémantique des bâtiments." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10281/document.
3D building models are widely used in the civil engineering industry. While the models are needed by several applications, such as architectural representations and simulation processes, they often lack of information that are of major importance for the consistency of the calculations. The original models are then often rebuilt in the way that fits better to the intended applications. To overcome this drawback, we introduce a framework allowing to enrich a 3D model of a building presenting just a geometry, in a way more interoperable model, by adding to it topological and semantic information. A cellular subdivision of the building space is first performed relying on its geometry, then the topological relationships between the cells are explicitely defined. Semantic labels are then attributed to the identified components based on the topology and defined heuristic rules. A 3D combinatorial map data structure (3-map) is used to handle the reconstructed information. From the enriched model we show how to extract applications-driven information allowing to perform acoustic simulation and indoor ray tracing navigation. The approach stands as a bridge between the modeling approaches and the applications in building analysis using the model. It is fully automatic and present interesting results on several types of building models
Pacheco-Martínez, Ana María. "Extracting cell complexes from 4-dimensional digital images." Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2262/document.
A digital image can be defined as a set of n-xels on a grid made up by n-cubes. Segmentation consists in computing a partition of an image into regions. The n-xels having similar characteristics (color, intensity, etc.) are regrouped. Schematically, each n-xel is assigned a label, and each region of the image is made up by n-xels with the same label. The methods "type" Marching cubes and Kenmochi et al. construct complexes representing the topology of the region of interest of a 3-dimensional binary digital image. In the first method, the algorithm constructs a simplicial complex, whose 0-cells are points of the edges of the dual grid. Inthe second one, the authors construct a cell complex on a dual grid, i.e. the 0-cells of the complex are vertices of the dual grid. In order to construct the complex, Kenmochi et al. compute (up to rotations) the different configurations of white and black vertices of a cube, and then, they construct the convex hulls of the black points of these configurations. These convex hulls define the cells of the complex, up to rotations. The work developed in this thesis extends Kenmochi et al. method todimension 4. The goal is to construct a cell complex from a binary digital image defined on a dual grid. First, we compute the different configurations of white and black vertices of a 4-cube, up to isometries, and then, we construct the convex hulls defined by these configurations. These convex hulls are constructed by deforming the original 4-cube, and we distinguishseveral basic construction operations (deformation, degeneracy of cells, etc.). Finally, we construct the cell complex corresponding to the dual image by assembling the cells so o
Una imagen digital puede ser definida como un conjunto de n–xeles en un mallado constituido de n–cubos. Los n–xeles pueden ser identificados con: (1) los n–cubos del mallado, o con (2) los puntos centrales de estos n–cubos. En el primer caso, trabajamos con un mallado primal, mientras que en el segundo, trabajamos con un mallado dual construido a partir del mallado primal. La segmentación consiste en calcular una partición de una imagen en regiones. Los n–xeles que tienen características similares (color, intensidad, etc.) son reagrupados. Esquemáticamente, a cada n–xel se le asocia una etiqueta, y cada región de la imagen está constituida de n–xeles con la misma etiqueta. En particular, si las únicas etiquetas permitidas para los n–xeles son “blanca” y “negra”, la segmentación se dice binaria: los n–xeles negros forman el primer plano (foreground) o región de interés en cuestión de análisis de la imagen, y los n–xeles blancos forman el fondo (background). Ciertos modelos, como los Grafos de Adyacencia de Regiones (RAGs), los Grafos Duales (DGs) y la carta topológica, han sido propuestos para representar las particiones en regiones, y en particular para representar la topología de estas regiones, es decir las relaciones de incidencia y/o adyacencia entre las diferentes regiones. El RAG [27] es un precursor de este tipo de modelos, y ha sido una fuente de inspiración de los DGs [18] y de la carta topológica [9, 10]. Un RAG representa una imagen primal etiquetada por un grafo: los vértices del grafo corresponden a regiones de la imagen, y las aristas del grafo representan las relaciones de adyacencia entre la regiones. Los DGs son un modelo que permite resolver ciertos inconvenientes de los RAGs para representar imágenes de dimensión 2. La carta topológica es una extensión de los modelos anteriores definida para manipular imágenes primales de dimensión 2 y 3, representando no solamente las relaciones topológicas, sino también las relaciones geométricas
Dovgal, Sergey. "An interdisciplinary image of Analytic Combinatorics." Thesis, Paris 13, 2019. http://www.theses.fr/2019PA131065.
This thesis is devoted to the development of tools and the use of methods from Analytic Combinatorics, including exact and asymptotic enumeration, statistical properties of random objects, and random generation.The key ingredient is the multidisciplinarity of the domain, which is emphasised by using examples from computational logic, statistical mechanics, biology, mathematical statistics, networks and queueing theory
Janaqi, Stefan. "Quelques éléments de la géométrie des graphes : graphes médians, produits d'arbres, génération convexe des graphes de Polymino." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1995GRE10093.
Jacques, Isabelle. "Aspects combinatoires en modélisation 2D et 3D et application à l'énumération des cartes et des solides." Mulhouse, 1991. http://www.theses.fr/1991MULH0185.
Books on the topic "Combinatoire géométrique":
Grötschel, Martin. Geometric algorithms and combinatorial optimization. 2nd ed. Berlin: Springer-Verlag, 1993.
Grötschel, Martin. Geometric algorithms and combinatorial optimization. Berlin: Springer-Verlag, 1988.
Orlik, Peter. Introduction to arrangements. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1989.
Deledicq, André. Le monde des pavages. 2nd ed. [Paris]: ACL-Éditions du Kangourou, 1997.
E, Goodman Jacob, and O'Rourke Joseph, eds. Handbook of discrete and computational geometry. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2004.
Pach, Janos. Thirty Essays on Geometric Graph Theory. New York, NY: Springer New York, 2013.
Agarwal, Pankaj K. Intersection and decomposition algorithms for planar arrangements. Cambridge: Cambridge University Press, 1991.
Kisačanin, Branislav. Mathematical problems and proofs: Combinatorics, number theory, and geometry. New York: Plenum Press, 1998.
Kisačanin, Branislav. Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry. Cleveland: Kluwer Academic Publishers, 2002.
JCDCG 2004 (2004 Tokyo, Japan). Discrete and computational geometry: Japanese conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004 : revised selected papers. Berlin: Springer, 2005.
Book chapters on the topic "Combinatoire géométrique":
"Géométrie et combinatoire." In CRM Monograph Series, 1. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/crmm/031/01.