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Bruhat order of symmetric groups and permutation tableaux
- Alternative Title
- Jisun Lim
- Author(s)
- 임지선
- Alternative Author(s)
- Jisun Lim
- Advisor
- 조수진
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2014-02
- Language
- eng
- 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.
- Alternative Abstract
- 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.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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