Screen LibraryAnalytic combinatorics in several variables /
"Mathematicians have found it useful to enumerate all sorts of things arising in discrete mathematics: elements of finite groups, configurations of ones and zeros, graphs of various sorts; the list is endless. Analytic combinatorics uses analytic techniques to do the counting: generating functi...
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| Main Authors: | |
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| Group Author: | |
| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge : |
| Publication Dates: | 2013. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ;
140 |
| Subjects: | |
| Summary: |
"Mathematicians have found it useful to enumerate all sorts of things arising in discrete mathematics: elements of finite groups, configurations of ones and zeros, graphs of various sorts; the list is endless. Analytic combinatorics uses analytic techniques to do the counting: generating functions are defined and their coefficients are then estimated via complex contour integrals. This book is the result of nearly fifteen years work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first b |
| Carrier Form: | xiii, 380 pages ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 363-371) and indexes. |
| ISBN: |
9781107031579 (hardback) : 1107031575 (hardback) |
| Index Number: | QA164 |
| CLC: | O157 |
| Call Number: | O157/P393 |
| Contents: | 1. Introduction -- 2. Generating functions -- 3. Univariate asymptotics -- 4. Fourier-Laplace integrals in one variable -- 5. Fourier-Laplace integrals in more than one variable -- 6. Techniques of symbolic computation via Gröbner bases -- 7. Cones, Laurent series and amoebas -- 8. Overview of analytic methods for multivariate generating functions -- 9. Smooth point asymptotics --10. Multiple point asymptotics --11. Cone point asymptotics --12. Worked examples -- 13. Extensions -- Appendices. |