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Analytic combinatorics in several va...

Pemantle, Robin.

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Analytic combinatorics in several variables /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Analytic combinatorics in several variables // Robin Pemantle, Mark C. Wilson.
作者:	Pemantle, Robin.
其他作者:	Wilson, Mark C.
出版者:	Cambridge :Cambridge University Press, : 2013.,
面頁冊數:	xiii, 380 p. :ill ;24 cm.
內容註:	Morse theory --
標題:	Combinatorial enumeration problems. -
電子資源:	http://assets.cambridge.org/97811070/31579/cover/9781107031579.jpg
ISBN:	9781107031579 (hbk.) :

Analytic combinatorics in several variables /
Pemantle, Robin.

Analytic combinatorics in several variables /Robin Pemantle, Mark C. Wilson. - Cambridge :Cambridge University Press,2013. - xiii, 380 p. :ill ;24 cm. - Cambridge studies in advanced mathematics ;140.

Includes bibliographical references (p. 363-371) and indexes.

Morse theory -- Introduction -- Combinatorial Enumeration --

"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"--

ISBN: 9781107031579 (hbk.) :US70.00

LCCN: 2012049386Subjects--Topical Terms:

706042
Combinatorial enumeration problems.

LC Class. No.: QA164.8 / .P46 2013

Dewey Class. No.: 511/.6

Analytic combinatorics in several variables /
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245 1 0 $a Analytic combinatorics in several variables / $c Robin Pemantle, Mark C. Wilson.
260 # $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a xiii, 380 p. : $b ill ; $c 24 cm.
490 1 0 $a Cambridge studies in advanced mathematics ; $v 140
504 $a Includes bibliographical references (p. 363-371) and indexes.
505 0 # $g Combinatorial Enumeration -- $t Introduction -- $t Generating functions -- $t Univariate asymptotics -- $g Mathematical Background -- $t Saddle integrals in one variable -- $t Saddle integrals in more than one variable -- $t Techniques of symbolic computation via Grobner bases -- $t Cones, Laurent series and amoebas -- $g Multivariate Enumeration -- $t Overview of analytic methods for multivariate generating functions -- $t Smooth point asymptotics -- $t Multiple point asymptotics -- $t Cone point asymptotics -- $t Worked examples -- $t Extensions -- $g Appendices -- $t Integration on Manifolds -- $a Morse theory -- $t Stratification and stratified Morse theory.
520 # $a "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"-- $c Provided by publisher.
650 # 0 $a Combinatorial enumeration problems. $3 706042
650 # 0 $a Functions of several complex variables. $3 526094
700 1 # $a Wilson, Mark C. $q (Mark Curtis), $d 1967- $3 2010654
856 4 2 $3 Cover image $u http://assets.cambridge.org/97811070/31579/cover/9781107031579.jpg