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

节省

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

陈腐思想

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

愤怒事实

执

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 .?