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

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A Gallery of Discrete Volumeseger points . form a lattice in ., and we often call the integer points .. This chapter carries us through concrete examples of lattice-point enumeration in various infinite families of integral and rational polytopes, and we will realize that many well-known families of numbers and polynomials, suc

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Finite Fourier Analysis the integers can be written as a polynomial in the .. root of unity .. Such a representation for .(.) is called a .. Here we develop finite Fourier theory using rational functions and their partial fraction decomposition. We then define the . and the . of finite Fourier series, and show how one can

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Zonotopesss of integral polytopes whose discrete volume is more tractable, and yet robust enough to be “closer” in complexity to generic integral polytopes. One initial class of more tractable polytopes is that of parallelepipeds, and as we will see, the Ehrhart polynomial of a .-dimensional half-open intege

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-Polynomials and ,,-Polynomialsoded in an Ehrhart polynomial is equivalent to the information encoded in its Ehrhart series. More precisely, when the Ehrhart series is written as a rational function, we introduced the name .. for its numerator: . Our goal in this chapter is to prove several decomposition formulas for . based on t

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Euler–Maclaurin Summation in ℝdon 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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