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Coefficient Asymptotics of Multivariable Algebraic Power Series and Rational Power Series With Pseudo Multiple Points
Coefficient Asymptotics of Multivariable Algebraic Power Series and Rational Power Series With Pseudo Multiple Points
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151334
- ISBN
- 9798382835082
- DDC
- 510
- 저자명
- Jin, Kaitian.
- 서명/저자
- Coefficient Asymptotics of Multivariable Algebraic Power Series and Rational Power Series With Pseudo Multiple Points
- 발행사항
- [Sl] : University of Pennsylvania, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 238 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Pemantle, Robin.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2024.
- 초록/해제
- 요약Analytic combinatorics in several variables (ACSV) generalizes the coefficient extraction of generating functions in one variable to several variables. Current developments in ACSV mostly concern rational or meromorphic generating functions by first representing coefficients via the multivariate Cauchy integral formula and then using Morse-theoretic homology arguments to deform the integral chain so that the integral becomes a sum of saddle point integrals. Coefficient asymptotics are previously known in the case when critical points of the Morse function are smooth points [PW02], multiple points [PW04, BMP24b], and quadratic cone points [BP11]. We generalize the result for multiple points to pseudo multiple points and show that these two kinds of points are similar under some conditions. The complexity hierarchy of ACSV goes up from rational functions to algebraic functions. By embedding the coefficient for an algebraic generating function as an elementary diagonal of a rational generating function with one more variable, [GMRW22] shows that the problem can be reduced to the well-known case of rational generating functions. We take a different approach, by lifting the torus in the Cauchy integral formula to the surface of the defining polynomial of the algebraic function, taking advantage of the covering space property of the surface. This leads to a similar computation to [GMRW22], avoids the Morse-theoretic homology arguments, and brings brighter transparency.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798382835082
■035 ▼a(MiAaPQ)AAI31241644
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aJin, Kaitian.
■24510▼aCoefficient Asymptotics of Multivariable Algebraic Power Series and Rational Power Series With Pseudo Multiple Points
■260 ▼a[Sl]▼bUniversity of Pennsylvania▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a238 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Pemantle, Robin.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2024.
■520 ▼aAnalytic combinatorics in several variables (ACSV) generalizes the coefficient extraction of generating functions in one variable to several variables. Current developments in ACSV mostly concern rational or meromorphic generating functions by first representing coefficients via the multivariate Cauchy integral formula and then using Morse-theoretic homology arguments to deform the integral chain so that the integral becomes a sum of saddle point integrals. Coefficient asymptotics are previously known in the case when critical points of the Morse function are smooth points [PW02], multiple points [PW04, BMP24b], and quadratic cone points [BP11]. We generalize the result for multiple points to pseudo multiple points and show that these two kinds of points are similar under some conditions. The complexity hierarchy of ACSV goes up from rational functions to algebraic functions. By embedding the coefficient for an algebraic generating function as an elementary diagonal of a rational generating function with one more variable, [GMRW22] shows that the problem can be reduced to the well-known case of rational generating functions. We take a different approach, by lifting the torus in the Cauchy integral formula to the surface of the defining polynomial of the algebraic function, taking advantage of the covering space property of the surface. This leads to a similar computation to [GMRW22], avoids the Morse-theoretic homology arguments, and brings brighter transparency.
■590 ▼aSchool code: 0175.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aAnalytic combinatorics
■653 ▼aAsymptotic enumeration
■653 ▼aCoefficient extraction
■653 ▼aGenerating functions
■653 ▼aMorse-theoretic homology
■690 ▼a0405
■690 ▼a0364
■71020▼aUniversity of Pennsylvania▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161282▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
