Connections Between Bases of Noncommutative Symmetric Functions
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Item Details
- title
- Connections Between Bases of Noncommutative Symmetric Functions
- author
- Sphar, Andrew Michael
- abstract
- In this thesis, we provide new formulae for converting immaculate noncommutative symmetric functions (NSym) indexed by compositions of length three into the ribbon basis of NSym, and provide a general result on the appearance of certain terms in the expansion of immaculate functions into the ribbon basis. We also examine a generalized definition of ribbon functions indexed by weak compositions, and how such functions can be reduced to ribbon functions indexed by compositions. Additionally, we show that the forgetful map on NSym maps skew immaculate functions to skew Schur symmetric functions when skew immaculate functions are defined using a Jacobi-Trudi identity.
- subject
- algebraic combinatorics
- immaculate functions
- noncommutative symmetric functions
- symmetric functions
- contributor
- Mason, Sarah K. (advisor)
- Allen, Edward (committee member)
- Bourdon, Abbey M. (committee member)
- date
- 2025-06-24T08:36:34Z (accessioned)
- 2025-06-24T08:36:34Z (available)
- 2025 (issued)
- degree
- Mathematics (discipline)
- identifier
- http://hdl.handle.net/10339/111028 (uri)
- language
- en (iso)
- publisher
- Wake Forest University
- type
- Thesis