Shifted Poirier-Reutenauer algebra corresponding to mixed insertion
- 발행기관 서강대학교 일반대학원
- 지도교수 오영탁
- 발행년도 2018
- 학위수여년월 2018. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000062847
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
In this thesis, we introduce a quotient algebra MPR of Malvenuto-Reutenauer algebra MR by using the mixed insertion algorithm due to Serrano. It may be viewed as a dual version of Shifted Poirier-Reutenauer algebra, which has been constructed by using Sagan-Worley insertion, in the sense that Serrano's mixed insertion is dual to Sagan-Worley insertion. Since it was shown by Jing and Li that NSym, the algebra of non-commutative symmetric functions, can be embedded into Malvenuto-Reutenauer algebra, we naturally obtain an algebra homomorphism from NSym to MPR. We also study the quotient of NSym by the kernel of this algebra homomorphism to demonstrate the relation between NSym and MPR.
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