Combinatorial approach to shifted Littlewood-Richardson coefficients : combinatorial models and a shifted tableau switching
- 발행기관 서강대학교 일반대학원
- 지도교수 오영탁
- 발행년도 2015
- 학위수여년월 2015. 2
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000055613
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
This thesis consists of two main parts related to shifted Littlewood-Richardson coefficients which appear in the expansion of the product of two Schur P-functions. In the first part, we establish bijections among three combinatorial models for the shifted Littlewood-Richardson coefficients: Littlewood-Richardson-Stembridge tableaux, \lambda-good semistandard decomposition tableaux, and shifted Littlewood-Richardson decomposition tableaux. In the second part, we introduce a shifted switching algorithm, which can be viewed as a shifted analog of the ordinary switching algorithm due to Benkart, Sottile and Stroomer. Similar to the ordinary case, our shifted switching algorithm enable us to explain various combinatorial identities associated to shifted Littlewood-Richardson coefficients.
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