Titlebook: Computing the Continuous Discretely; Integer-Point Enumer Matthias Beck,Sinai Robins Textbook 2015Latest edition Matthias Beck and Sinai Ro

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Maddie Breeze,Yvette Taylor,Cristina CostaMichel Brion. The power of .—the centerpiece of this chapter—has been applied to various domains, such as . in integer linear programming, and to higher-dimensional ., which we study in Chapter . In a sense, Brion’s theorem is the natural extension of the familiar finite geometric series identity .

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https://doi.org/10.1007/978-3-319-53725-2on is the difference between the discrete integer-point transform and its continuous sibling: . where we have replaced the variable . that we have commonly used in generating functions by an exponential variable. Note that on setting . = 0 in (12.2), we obtain the difference between the discrete and

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https://doi.org/10.1007/978-94-017-3536-0rtion of space that the cone . occupies. In slightly different words, if we pick a point . “at random,” then the probability that . is precisely the solid angle at the apex of .. Yet another view of solid angles is that they are in fact volumes of spherical polytopes: the region of intersection of a

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Computing the Continuous Discretely978-1-4939-2969-6Series ISSN 0172-6056 Series E-ISSN 2197-5604

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Matthias Beck,Sinai RobinsNew edition extensively revised and updated.Places a strong emphasis on computational techniques.Contains more than 200 exercises, including hints to selected exercises.Includes supplementary material

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