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Bruhat order of symmetric groups and permutation tableaux
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 조수진 | - |
| dc.contributor.author | 임지선 | - |
| dc.date.accessioned | 2018-11-08T08:12:34Z | - |
| dc.date.available | 2018-11-08T08:12:34Z | - |
| dc.date.issued | 2014-02 | - |
| dc.identifier.other | 16583 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/11708 | - |
| dc.description | 학위논문(석사)--아주대학교 일반대학원 :수학과,2014. 2 | - |
| dc.description.abstract | Coxeter군과 그 위에 정의된 Bruhat 순서를 소개하고 기본적인 성질을 살펴본다. 가장 잘 알려진 Coxeter군인 대칭군과 대칭군에서의 Bruhat 순서를 이해하는 알려진 조합적 방법을 소개한다. 본 논문에서는 대칭군의 원소와 일대일 대응관계에 있는 순열타블로를 이용하여 대칭군에서의 Bruhat 순서를 조합적으로 이해하고자 하였으며, 두 순열이 반드시 Bruhat순서관계에 있을 조건과 순서관계에 있을 수 없는 조건을 순열타블로를 이용하여 제시하였다. | - |
| dc.description.tableofcontents | 1 Introduction 4 2 Coxeter system and Bruhat order 6 2.1 Coxeter system 6 2.2 Bruhat order 10 2.2.1 Basic properties of Bruhat order 12 3 Symmetric group 14 3.1 Symmetric group as a Coxeter group 14 3.2 Bruhat order of symmertric group 16 4 Permutation tableaux 20 4.1 Permutation tableaux 20 4.2 Bruhat order in permutation tableaux 24 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | Bruhat order of symmetric groups and permutation tableaux | - |
| dc.title.alternative | Jisun Lim | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.alternativeName | Jisun Lim | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2014. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 608355 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000016583 | - |
| dc.description.alternativeAbstract | In this study, we try to understand Bruhat order of symmetric groups in terms of permutation tableaux. Bruhat order is a partial order on Coxeter groups and symmetric group is a well known Coxeter group. We first observe the idea to understand Bruhat order by using combinatorial method with original diagram and tableaux, and then we try to find a new criterion to check the comparability in Bruhat order in terms of permutation tableaux. We make some observations on Bruhat order of the symmetric groups in terms of permutation tableaux: one gives a condition when two permutation tableaux are comparable and the other gives a condition when two permutation tableaux are not comparable. We include the diagrams of Bruhat order on S_4 and S_5 in terms of permutation tableaux also. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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