Rectangle tilings, connectivity and associated covariants

Diplôme Thèse Rectangle tilings, connectivity and associated covariants eng 2013-06-20 author Shekhawat Krishnendra 682358 director Coray Daniel 26390 10.13097/archive-ouverte/unige:29531 urn:nbn:ch:unige-295312 Sc. 4570 In this work, we focus on Tiling by rectangles, its Connectivity and associated Covariants. Tiling by rectangles is the geometric problem of arranging a given family of rectangles in a larger specific frame. A primitive version is rectangle tiling. Then the notion of rectangle tiling is extended to tiling rectangles inside some other shapes. This generalization is achieved through another object of a mathematical nature, namely the allocation matrix. This problem also involves the study of another mathematical concept the extra spaces which are introduced in the geometric distribution process. When tiling by rectangles, an effort has been made to obtain a tiling which is best from the point of view of connectivity. To refine the number of solutions originating from the algorithm, we have studied and developed several covariants related to tilings and their graph. The presented research work opens a new field for applied mathematicians, in that it combines various aspects of geometry, topology, graph theory and optimization theory, towards the solution of a problem which is well known to architects, but which has rarely been attacked by mathematical methods. Dewey 510 25 Section de mathématiques 11 false 72ffe91f-ef7f-40fc-b347-34a8249a7749 Thesis Public Thesis_KS (2).pdf 1461977 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Shekhawat, Krishnendra