Analytic combinatorics in several variables. (Q2856004)
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scientific article; zbMATH DE number 6218356
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analytic combinatorics in several variables. |
scientific article; zbMATH DE number 6218356 |
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23 October 2013
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analytic combinatorics
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generating functions
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Analytic combinatorics in several variables. (English)
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The book describes the recent progress of analytic combinatorics, which refers to ``the use of complex anaytic methods to solve problems in combinatorial enumeration'', by means of the study of generating functions. The main progress made from the 1990s (when the theory was ``in its infancy'') up to now are described, including mainly asymptotic results in one variable (Part I) and many variables (Part III). NEWLINENEWLINENEWLINEThe book also discusses the necessary mathematical background in detail, such as Fourier-Laplace integrals, Laurent series and Gröbner bases (Part II), integration on manifolds and Morse theory (Part IV).
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