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

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Euler–Maclaurin Summation in ?d the continuous volumes of .. Relations between the two quantities . and . are known as . formulas for polytopes. The “behind-the-scenes” operators that are responsible for affording us with such connections are the differential operators known as ., whose definition utilizes the Bernoulli numbers in a surprising way.

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Solid Angles cone with a sphere. There is a theory, which we will develop in this chapter and which goes back to I.G. Macdonald, that parallels the Ehrhart theory of Chapters . and ., with some genuinely new ideas.

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https://doi.org/10.1007/978-1-349-20865-4 there a “good formula” for .. as a function of .? Are there identities involving various ..’s? Embedding this sequence into the . . allows us to retrieve answers to the questions above in a surprisingly quick and elegant way. We may think of .(.) as lifting our sequence .. from its discrete setting

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https://doi.org/10.1007/3-540-60941-5eger 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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Lecture Notes in Computer Scienceosely speaking, a magic square is an . × . array of integers (usually required to be positive, often restricted to the numbers ., usually required to have distinct entries) whose sum along every row, column, and main diagonal is the same number, called the .. Magic squares have turned up time and ag

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Time Travel in World Literature and Cinema 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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https://doi.org/10.1007/978-94-017-3530-8y of the coin-exchange problem in Chapter?. They have one shortcoming, however (which we shall remove): the definition of .(.,?.) requires us to sum over . terms, which is rather slow when .?=?2., for example. Luckily, there is a magical . for the Dedekind sum .(.,?.) that allows us to compute it in

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Akitaka Dohtani,Toshio Inaba,Hiroshi Osakaoded 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