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<図書>
Analytic combinatorics in several variables

責任表示 Robin Pemantle, Mark C. Wilson
シリーズ Cambridge studies in advanced mathematics ; 140
データ種別 図書
出版者 Cambridge [England] : Cambridge University Press
出版年 2013
本文言語 英語
大きさ xiii, 380 p. : ill. ; 24 cm
概要 "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"--続きを見る
目次 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.
電子版へのリンク

所蔵情報

: hardback 理系図3F 数理独自 033212013002455 PEMA/10/1 2013

書誌詳細

一般注記 Includes bibliographical references (p. 363-371) and indexes
著者標目 Pemantle, Robin
Wilson, Mark C. (Mark Curtis), 1967-
件 名 LCSH:Combinatorial enumeration problems
LCSH:Functions of several complex variables
FREE:MATHEMATICS / Discrete Mathematics. bisacsh
分 類 LCC:QA164.8
DC23:511/.6
書誌ID 1001509068
ISBN 9781107031579
NCID BB12722477
巻冊次 : hardback ; ISBN:9781107031579
登録日 2013.06.25
更新日 2017.03.14

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