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

節(jié)省

A Gallery of Discrete Volumesion in various infinite families of integral and rational polytopes, and we will realize that many well-known families of numbers and polynomials, such as Bernoulli and Stirling numbers, make an appearance as the lattice-point enumerators of some concrete families of polytopes.

milligram

陳腐思想

Finite Fourier Analysisheory using rational functions and their partial fraction decomposition. We then define the . and the . of finite Fourier series, and show how one can use these ideas to prove identities on trigonometric functions, as well as find connections to the classical ..

Truculent

Expostulate

叫喊

憤怒事實(shí)

執(zhí)

https://doi.org/10.1007/978-3-319-53725-2 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.

Conflagration

set598

The Coin-Exchange Problem of Frobenius into the continuous world of functions. We introduce techniques for working with generating functions, and we use them to shed light on the .: Given relatively prime positive integers ., what is the largest integer that cannot be written as a nonnegative integral linear combination of .?