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＜電子ブック＞
Triangulations : Structures for Algorithms and Applications / by Jesus De Loera, Joerg Rambau, Francisco Santos
(Algorithms and Computation in Mathematics ; 25)

版	1st ed. 2010.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2010
大きさ	X, 539 p. 496 illus., 281 illus. in color : online resource
著者標目	*De Loera, Jesus author Rambau, Joerg author Santos, Francisco author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Discrete mathematics LCSH:Computer science LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Computer science—Mathematics LCSH:Mathematics—Data processing FREE:Algebraic Geometry FREE:Discrete Mathematics FREE:Theory of Computation FREE:Convex and Discrete Geometry FREE:Mathematics of Computing FREE:Computational Mathematics and Numerical Analysis
一般注記	Triangulations in Mathematics -- Configurations, Triangulations, Subdivisions, and Flips -- Life in Two Dimensions -- A Tool Box -- Regular Triangulations and Secondary Polytopes -- Some Interesting Configurations -- Some Interesting Triangulations -- Algorithmic Issues -- Further Topics Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensive treatment of the theory of secondary polytopes and related topics. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulations or finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly five hundred illustrations, the book gently guides readers through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice polytopes) and "pathological" (e.g., disconnected spaces of triangulations) situations using only elementary principles HTTP:URL=https://doi.org/10.1007/978-3-642-12971-1

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