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Combinatorics of Vexillary Grothendieck Polynomials.
Combinatorics of Vexillary Grothendieck Polynomials.
상세정보
- 자료유형
- 학위논문
- Control Number
- 0017161332
- International Standard Book Number
- 9798382843681
- Dewey Decimal Classification Number
- 510
- Main Entry-Personal Name
- Hafner, Elena Sarah.
- Publication, Distribution, etc. (Imprint
- [S.l.] : Cornell University., 2024
- Publication, Distribution, etc. (Imprint
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- Physical Description
- 89 p.
- General Note
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- General Note
- Advisor: Meszaros, Karola.
- Dissertation Note
- Thesis (Ph.D.)--Cornell University, 2024.
- Summary, Etc.
- 요약First introduced by Lascoux and Schutzenberger in 1982, Grothendieck polynomials are a family of polynomials indexed by permutations in Sn. In this thesis, we study the supports of Grothendieck polynomials associated to vexillary (2143-avoiding) permutations. We use bumpless pipe dreams to show several nice properties of the supports of vexillary Grothendieck polynomials, addressing special cases of conjectures of Meszaros, Setiabrata, and St. Dizier. Additionally, through joint work with Meszaros, Setiabrata, and St. Dizier, we showthat the homogenized Grothendieck polynomial associated to any vexillary per-mutation is M-convex. To accomplish this, we introduce bubbling diagrams and show that they compute the supports of vexillary Grothendieck polynomials.
- Subject Added Entry-Topical Term
- Mathematics.
- Subject Added Entry-Topical Term
- Theoretical mathematics.
- Index Term-Uncontrolled
- Grothendieck , Alexander
- Index Term-Uncontrolled
- Vexillary Grothendieck polynomials
- Index Term-Uncontrolled
- Permutations
- Index Term-Uncontrolled
- Polytopes
- Index Term-Uncontrolled
- Bumpless pipe dreams
- Added Entry-Corporate Name
- Cornell University Mathematics
- Host Item Entry
- Dissertations Abstracts International. 85-12B.
- Electronic Location and Access
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:658387
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798382843681
■035 ▼a(MiAaPQ)AAI31242232
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aHafner, Elena Sarah.▼0(orcid)0009-0004-4807-1710
■24510▼aCombinatorics of Vexillary Grothendieck Polynomials.
■260 ▼a[S.l.]▼bCornell University. ▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a89 p.
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Meszaros, Karola.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aFirst introduced by Lascoux and Schutzenberger in 1982, Grothendieck polynomials are a family of polynomials indexed by permutations in Sn. In this thesis, we study the supports of Grothendieck polynomials associated to vexillary (2143-avoiding) permutations. We use bumpless pipe dreams to show several nice properties of the supports of vexillary Grothendieck polynomials, addressing special cases of conjectures of Meszaros, Setiabrata, and St. Dizier. Additionally, through joint work with Meszaros, Setiabrata, and St. Dizier, we showthat the homogenized Grothendieck polynomial associated to any vexillary per-mutation is M-convex. To accomplish this, we introduce bubbling diagrams and show that they compute the supports of vexillary Grothendieck polynomials.
■590 ▼aSchool code: 0058.
■650 4▼aMathematics.
■650 4▼aTheoretical mathematics.
■653 ▼aGrothendieck , Alexander
■653 ▼aVexillary Grothendieck polynomials
■653 ▼aPermutations
■653 ▼aPolytopes
■653 ▼aBumpless pipe dreams
■690 ▼a0405
■690 ▼a0642
■71020▼aCornell University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161332▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
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