Titlebook: Computing the Continuous Discretely; Integer-point Enumer Matthias Beck,Sinai Robins Textbook 20071st edition Springer-Verlag New York 2007

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Dedication

Affectation

Euler—Maclaurin Summation in ℝThus far we have often been concerned with the difference between the discrete volume of a polytope . and its continuous volume. In other words, the quantity

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ventilate

Ralston Anthony,Rabinowitz Philipnteger points ℤ. form a lattice in ℝ., and we often call the integer points .. This chapter carries us through concrete instances of lattice-point enumeration in various integral and rational polytopes. There is a tremendous amount of research taking place along these lines, even as the reader is lo

entreat

https://doi.org/10.1007/3-540-15202-4 which give linear relations among the face numbers .. They are called ., in honor of their discoverers Max Wilhelm Dehn (1878–1952) and Duncan MacLaren Young Sommerville (1879–1934). Our second goal is to unify the Dehn—Sommerville relations (Theorem 5.1 below) with Ehrhart—Macdonald reciprocity (T

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Function STITLE function WTITLE,in-exchange problem in Chapter 1. They have one shortcoming, however (which we‘ll 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 roughly log. (.) =

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