节省 发表于 2025-3-25 05:24:32
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 发表于 2025-3-25 08:06:24
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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 发表于 2025-3-25 18:31:41
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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 发表于 2025-3-26 14:07:05
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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 .?