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Analytic combinatorics in several va...

Pemantle, Robin.

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Analytic combinatorics in several variables

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analytic combinatorics in several variables/ Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.
Author:	Pemantle, Robin.
other author:	Wilson, Mark C.
Published:	Cambridge :Cambridge University Press, : 2013.,
Description:	xiii, 380 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Combinatorial enumeration problems. -
Online resource:	https://doi.org/10.1017/CBO9781139381864
ISBN:	9781139381864

Analytic combinatorics in several variables
Pemantle, Robin.

Analytic combinatorics in several variables[electronic resource] /Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland. - Cambridge :Cambridge University Press,2013. - xiii, 380 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;140. - Cambridge studies in advanced mathematics ;140..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/ACSVbook/.

ISBN: 9781139381864Subjects--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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020 $a 9781139381864 $q (electronic bk.)
020 $a 9781107031579 $q (hardback)
020 $a 9781107471818 $q (paperback)
035 $a CR9781139381864
040 $a UkCbUP $b eng $c UkCbUP $d GP
041 0 $a eng
050 4 $a QA164.8 $b .P46 2013
082 0 4 $a 511.6 $2 23
090 $a QA164.8 $b .P393 2013
100 1 $a Pemantle, Robin. $3 2010653
245 1 0 $a Analytic combinatorics in several variables $h [electronic resource] / $c Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland.
260 $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a xiii, 380 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 140
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 8 $a 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.
520 $a This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/ACSVbook/.
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 3470471
830 0 $a Cambridge studies in advanced mathematics ; $v 140. $3 3470472
856 4 0 $u https://doi.org/10.1017/CBO9781139381864