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作者 Pemantle, Robin
書名 Analytic combinatorics in several variables / Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland
出版項 Cambridge : Cambridge University Press, 2013
國際標準書號 9781107031579 (hardback)
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA164.8 P46 2013    在架上    30340200530925
說明 xiii, 380 pages ; 24 cm
text rdacontent
unmediated rdamedia
volume rdacarrier
系列 Cambridge studies in advanced mathematics ; 140
Cambridge studies in advanced mathematics ; 140
附註 "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 book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable"-- Provided by publisher
Includes bibliographical references (pages 363-371) and indexes
Machine generated contents note: Part I. Combinatorial Enumeration: 1. Introduction; 2. Generating functions; 3. Univariate asymptotics; Part II. Mathematical Background: 4. Saddle integrals in one variable; 5. Saddle integrals in more than one variable; 6. Techniques of symbolic computation via Grobner bases; 7. Cones, Laurent series and amoebas; Part III. Multivariate Enumeration: 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; Part IV. Appendices: Appendix A. Manifolds; Appendix B. Morse theory; Appendix C. Stratification and stratified Morse theory
主題 Combinatorial enumeration problems
Functions of several complex variables
MATHEMATICS / Discrete Mathematics. bisacsh
Alt Author Wilson, Mark C. (Mark Curtis), 1967-
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