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Several Problems in Extremal Combinatorics
Several Problems in Extremal Combinatorics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103534
- ISBN
- 9798280712645
- DDC
- 510
- 저자명
- Dong, Dingding.
- 서명/저자
- Several Problems in Extremal Combinatorics
- 발행사항
- [Sl] : Harvard University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 239 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Includes supplementary digital materials.
- 주기사항
- Advisor: Williams, Lauren.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2025.
- 초록/해제
- 요약This thesis presents three distinct contributions to extremal combinatorics. First, it resolves a conjecture by Bollobas, Brightwell, and Leader on the prevalence of unate k-SAT functions, proving that for all fixed k ≥ 2, almost all k-SAT functions on n variables are unate (i.e., monotone after negating certain variables).econd, it addresses a question posed by Sapozhenko on the enumeration of q-ary t-error correcting codes. Improving upon previous bounds, it demonstrates that for a broad range of parameters, the number of such codes is tightly bounded by the Hamming bound.Finally, it investigates the commonness and uncommonness of systems of linear equations over finite fields. Answering questions of Kamcev, Liebenau, and Morrison, it shows that all 2 x k linear systems with k even and girth k − 1 are uncommon over sufficiently large finite fields, and provides a near-complete classification of common 2 x 5 linear systems.This thesis provides new insights into the structure of various combinatorial objects and contributes to the broader understanding of extremal combinatorics.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Combinatorics
- 키워드
- Conjecture
- 키워드
- Hamming bound
- 키워드
- Finite fields
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■1001 ▼aDong, Dingding.▼0(orcid)0000-0001-8500-2897
■24510▼aSeveral Problems in Extremal Combinatorics
■260 ▼a[Sl]▼bHarvard University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a239 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aIncludes supplementary digital materials.
■500 ▼aAdvisor: Williams, Lauren.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2025.
■520 ▼aThis thesis presents three distinct contributions to extremal combinatorics. First, it resolves a conjecture by Bollobas, Brightwell, and Leader on the prevalence of unate k-SAT functions, proving that for all fixed k ≥ 2, almost all k-SAT functions on n variables are unate (i.e., monotone after negating certain variables).econd, it addresses a question posed by Sapozhenko on the enumeration of q-ary t-error correcting codes. Improving upon previous bounds, it demonstrates that for a broad range of parameters, the number of such codes is tightly bounded by the Hamming bound.Finally, it investigates the commonness and uncommonness of systems of linear equations over finite fields. Answering questions of Kamcev, Liebenau, and Morrison, it shows that all 2 x k linear systems with k even and girth k − 1 are uncommon over sufficiently large finite fields, and provides a near-complete classification of common 2 x 5 linear systems.This thesis provides new insights into the structure of various combinatorial objects and contributes to the broader understanding of extremal combinatorics.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aCombinatorics
■653 ▼aConjecture
■653 ▼aHamming bound
■653 ▼aFinite fields
■690 ▼a0405
■690 ▼a0364
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357598▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
