Analytic combinatorics in several variables:
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 es...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2013
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| Schriftenreihe: | Cambridge studies in advanced mathematics
140 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9781139381864 https://doi.org/10.1017/CBO9781139381864 https://doi.org/10.1017/CBO9781139381864 https://doi.org/10.1017/CBO9781139381864 |
| Zusammenfassung: | 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/ |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 Online-Ressource (xiii, 380 Seiten) |
| ISBN: | 9781139381864 |
| DOI: | 10.1017/CBO9781139381864 |
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| 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/ | ||
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Datensatz im Suchindex
| _version_ | 1818982566276890624 |
|---|---|
| any_adam_object | |
| author | Pemantle, Robin |
| author_GND | (DE-588)1044381353 (DE-588)1044382147 |
| author_facet | Pemantle, Robin |
| author_role | aut |
| author_sort | Pemantle, Robin |
| author_variant | r p rp |
| building | Verbundindex |
| bvnumber | BV043940787 |
| classification_rvk | SK 170 |
| collection | ZDB-20-CBO |
| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9781139381864 (OCoLC)967696463 (DE-599)BVBBV043940787 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139381864 |
| format | Electronic eBook |
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| id | DE-604.BV043940787 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:15Z |
| institution | BVB |
| isbn | 9781139381864 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349757 |
| oclc_num | 967696463 |
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| owner | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 Online-Ressource (xiii, 380 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Pemantle, Robin Verfasser (DE-588)1044381353 aut Analytic combinatorics in several variables Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland Cambridge Cambridge University Press 2013 1 Online-Ressource (xiii, 380 Seiten) txt rdacontent c rdamedia cr rdacarrier 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/ Combinatorial enumeration problems Functions of several complex variables Abzählende Kombinatorik (DE-588)4132720-2 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Abzählende Kombinatorik (DE-588)4132720-2 s 1\p DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 2\p DE-604 Wilson, Mark C. 1967- Sonstige (DE-588)1044382147 oth Erscheint auch als Druck-Ausgabe 978-1-107-03157-9 Erscheint auch als Druck-Ausgabe 978-1-107-47181-8 Cambridge studies in advanced mathematics 140 (DE-604)BV044781283 140 https://doi.org/10.1017/CBO9781139381864 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pemantle, Robin Analytic combinatorics in several variables Cambridge studies in advanced mathematics 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 Combinatorial enumeration problems Functions of several complex variables Abzählende Kombinatorik (DE-588)4132720-2 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4132720-2 (DE-588)4169285-8 |
| title | Analytic combinatorics in several variables |
| title_auth | Analytic combinatorics in several variables |
| title_exact_search | Analytic combinatorics in several variables |
| title_full | Analytic combinatorics in several variables Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland |
| title_fullStr | Analytic combinatorics in several variables Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland |
| title_full_unstemmed | Analytic combinatorics in several variables Robin Pemantle, The University of Pennsylvania, Mark C. Wilson, University of Auckland |
| title_short | Analytic combinatorics in several variables |
| title_sort | analytic combinatorics in several variables |
| topic | Combinatorial enumeration problems Functions of several complex variables Abzählende Kombinatorik (DE-588)4132720-2 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Combinatorial enumeration problems Functions of several complex variables Abzählende Kombinatorik Mehrere komplexe Variable |
| url | https://doi.org/10.1017/CBO9781139381864 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT pemantlerobin analyticcombinatoricsinseveralvariables AT wilsonmarkc analyticcombinatoricsinseveralvariables |