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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 沈俊嚴(Chun-Yen Shen) | |
| dc.contributor.author | Che-Jui Chang | en |
| dc.contributor.author | 張哲睿 | zh_TW |
| dc.date.accessioned | 2023-03-19T23:21:48Z | - |
| dc.date.copyright | 2022-07-05 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-06-19 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85697 | - |
| dc.description.abstract | 片秩法 (Slice Rank) 是 Croot, Lev 以及 Pach 於2016年提出的一個新的組合數學工具，許多極值組合學當中的問題都透過了這個方法有了新的進展。在這篇論文中，我們會介紹片秩法及其應用，同時我們也會介紹劃分秩法 (Partition Rank) 及其應用。最後我們會利用片秩法以及隨機圖的定理證明直角移除定理。 | zh_TW |
| dc.description.abstract | Slice rank methods are new combinatorial tools introduced by Croot, Lev, and Pach in 2016. Many problems in extremal combinatorics are improved by applying the slice rank methods. In this thesis, we'll introduce the slice rank methods and their applications. Moreover, the partition rank and one of its applications are also introduced. Finally, we use slice rank methods and a random graph theorem to prove the right angles removal lemma. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T23:21:48Z (GMT). No. of bitstreams: 1 U0001-1506202216024100.pdf: 833589 bytes, checksum: 4571e391ffc9bdbfaa5c686e77ba8e7c (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | 1 Introduction p.1 1.1 Background p.1 1.2 General notations p.1 2 Slice Rank of Functions and Its Applications p.2 2.1 Slice rank of functions p.2 2.2 Application 1: Capset problem p.5 2.3 Application 2: Solutions of particular linear systems p.7 2.4 Application 3: Largest right-angle-free subsets of Fnp p.13 3 Slice Rank of Tensors p.16 3.1 Tensor product of vector spaces p.16 3.2 Slice rank of tensors p.19 4 Partition Rank p.27 4.1 Definitions and basic properties p.27 4.2 Distinctness indicator function p.31 4.3 Application 4: Largest k-right-corner-free subsets of Fnp p.35 5 Right Angle Removal Lemma p.43 5.1 Background p.43 5.2 Main result and its proof p.43 Acknowledgement p.49 References p.50 | |
| dc.language.iso | en | |
| dc.subject | 移除引理 | zh_TW |
| dc.subject | 片秩法 | zh_TW |
| dc.subject | 劃分秩法 | zh_TW |
| dc.subject | 極值組合 | zh_TW |
| dc.subject | 直角 | zh_TW |
| dc.subject | slice rank | en |
| dc.subject | removal lemma | en |
| dc.subject | right angle | en |
| dc.subject | extremal combinatorics | en |
| dc.subject | partition rank | en |
| dc.title | 片秩法及其應用 | zh_TW |
| dc.title | Slice Rank Methods and Their Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 110-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.author-orcid | 0000-0001-9029-4687 | |
| dc.contributor.advisor-orcid | 沈俊嚴(0000-0003-0888-3007) | |
| dc.contributor.oralexamcommittee | 傅恆霖(Hung-Lin Fu),戴尚年(Shagnik Das) | |
| dc.contributor.oralexamcommittee-orcid | 傅恆霖(0000-0001-7218-3043) | |
| dc.subject.keyword | 片秩法,劃分秩法,極值組合,直角,移除引理, | zh_TW |
| dc.subject.keyword | slice rank,partition rank,extremal combinatorics,right angle,removal lemma, | en |
| dc.relation.page | 52 | |
| dc.identifier.doi | 10.6342/NTU202200962 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-06-21 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| dc.date.embargo-lift | 2022-07-05 | - |
| 顯示於系所單位： | 數學系 | |
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