서브메뉴
검색
A Polynomial Invariant of Partial Orders
A Polynomial Invariant of Partial Orders
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152018
- ISBN
- 9798384051299
- DDC
- 510
- 서명/저자
- A Polynomial Invariant of Partial Orders
- 발행사항
- [Sl] : Cornell University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 98 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Aguiar, Marcelo.
- 학위논문주기
- Thesis (Ph.D.)--Cornell University, 2024.
- 초록/해제
- 요약This thesis is built around a Hopf monoid structure on the linearized vector species PO of partial orders. In the third chapter, we present a cancellation-free antipode formula for PO, which we generalize in chapter 4 to the setting of A-species, where A is any simplicial hyperplane arrangement.In chapter 5, we study a polynomial invariant which is defined for any poset p, and whose value at 1 is the number of linear extensions of the poset. We prove that the polynomial invariant studied in [9] is a reparameterization of our polynomial invariant whenever p is (2+2)-free, from which it follows that the two polynomials have the same value at -1 whenever p is (2+2)-free. We use our antipode formula to prove a formula for the value of the polynomial invariant at -1 for all posets p which do not contain a (2+2)-subposet. In doing so, we define a class of simplicial complexes of independent interest.Chapter 6 is concerned with these simplicial complexes, and with proving a result about iteration of the nerve construction on finite simplicial complexes up to stabilization which we call the final nerve construction. This allows us to show that all interval simplicial complexes are homotopy equivalent to either balls or spheres, and to present a correspondence between pairs of finite simplicial complexes which are stable under the final nerve construction and equivalence classes of a certain family of (0,1)-matrices.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Monoid structure
- 기타저자
- Cornell University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017162485
■00520250211152018
■006m o d
■007cr#unu||||||||
■020 ▼a9798384051299
■035 ▼a(MiAaPQ)AAI31331940
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aConnolly-Whelan, John Henry.▼0(orcid)0000-0001-9556-3081
■24512▼aA Polynomial Invariant of Partial Orders
■260 ▼a[Sl]▼bCornell University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a98 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Aguiar, Marcelo.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aThis thesis is built around a Hopf monoid structure on the linearized vector species PO of partial orders. In the third chapter, we present a cancellation-free antipode formula for PO, which we generalize in chapter 4 to the setting of A-species, where A is any simplicial hyperplane arrangement.In chapter 5, we study a polynomial invariant which is defined for any poset p, and whose value at 1 is the number of linear extensions of the poset. We prove that the polynomial invariant studied in [9] is a reparameterization of our polynomial invariant whenever p is (2+2)-free, from which it follows that the two polynomials have the same value at -1 whenever p is (2+2)-free. We use our antipode formula to prove a formula for the value of the polynomial invariant at -1 for all posets p which do not contain a (2+2)-subposet. In doing so, we define a class of simplicial complexes of independent interest.Chapter 6 is concerned with these simplicial complexes, and with proving a result about iteration of the nerve construction on finite simplicial complexes up to stabilization which we call the final nerve construction. This allows us to show that all interval simplicial complexes are homotopy equivalent to either balls or spheres, and to present a correspondence between pairs of finite simplicial complexes which are stable under the final nerve construction and equivalence classes of a certain family of (0,1)-matrices.
■590 ▼aSchool code: 0058.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aPolynomial invariant
■653 ▼aReparameterization
■653 ▼aHyperplane arrangement
■653 ▼aMonoid structure
■690 ▼a0405
■690 ▼a0364
■71020▼aCornell University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17162485▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
