Triangulations - De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco


Structures for Algorithms and Applications

Jesús A. De Loera Jörg Rambau Francisco Santos 

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Triangulations appear everywhere, from the volume computations and meshing to algebra and topology. This book studies 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), as well as for setting up connections to applications in algebra, computer science, combinatorics, and optimization.

With many examples and exercises, and with almost five hundred illustrations, the book gently guides beginners 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.


  • Verlag: Springer, Berlin
  • 2010
  • Ausstattung/Bilder: 2010. x, 539 S. 215 SW-Abb., 281 Farbabb., 50 Tabellen, X, 539p. 496 illus., 281 illus. in color. 260 m
  • Algorithms and Computation in Mathematics Vol.25
  • Best.Nr. des Verlages: 12605583
  • Englisch
  • Abmessung: 271mm x 205mm x 33mm
  • Gewicht: 1468g
  • ISBN-13: 9783642129704
  • ISBN-10: 3642129706
  • Best.Nr.: 29378833
J.A. De Loera is a professor of mathematics at the University of California, Davis. His work approaches difficult computational problems in discrete mathematics and optimization using tools from algebra and convex geometry. His research has been recognized by an Alexander von Humboldt Fellowship and several national and international grants. He is an associate editor of the journal "Discrete Optimization".

Jörg Rambau is the chair professor of Wirtschaftsmathematik (Business Mathematics) at the Universität of Bayreuth since 2004. Before that he was associate head of the optimization department at the Zuse Institute Berlin (ZIB). His research encompasses problems in applied optimization, algorithmic discrete mathematics and combinatorial geometry. He is the creator of the state of the art program for triangulation computations TOPCOM. He is associate editor of the "Jahresberichte der Deutschen Mathematiker-Vereinigung".

Francisco Santos, a professor at the Universidad de Cantabria Spain, received the Young Researcher award from the Universidad Complutense de Madrid in 2003 and was an invited speaker in the Combinatorics Section of the International Congress of Mathematicians in 2006. He is well-known for his explicit constructions of polytopes with disconnected spaces of triangulations, some of which are featured in this book. He is an editor of Springer Verlag's journal "Discrete and Computational Geometry".

Blick ins Buch "Triangulations"


Rules for Notation.- 1 Triangulations in Mathematics.- 2 Configurations, Triangulations, Subdivisions, and Flips.- 3 Life in two Dimensions.- 4 A Tool Box.- 5 Regular Triangulations and Secondary Polytopes.- 6 Some Interesting Configurations.- 7 Some Interesting Triangulations.- 8 Algorithmic Issues.- 9 Further Topics.- Bibliography.- Index