1 option
Polynomiality of the Bigraded Subdimension of Diagonal Harmonics Xinxuan Wang
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Wang, Xinxuan, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Theoretical mathematics.
- 0405.
- 0642.
- Local Subjects:
- Mathematics.
- Theoretical mathematics.
- 0405.
- 0642.
- Physical Description:
- 1 electronic resource (61 pages)
- Contained In:
- Dissertations Abstracts International 86-12B
- Place of Publication:
- Ann Arbor : ProQuest Dissertations and Theses, 2025
- Language Note:
- English
- Summary:
- A sequence of Sn-representation Vn is called representation (multiplicity) stable if after some n, the irreducible decomposition of Vn stabilizes. In particular, Church, Ellenberg and Farb found that if we fix a and b, then the space of diagonal harmonics DHna,b exhibits this behavior, and its dimension stabilizes to a polynomial in n eventually. Building on this result, we use the Schedules Formula to get an explicit combinatorial polynomial for the dimension of the bigraded spaces DHna,b combinatorially. This derivation not only yields the dimension formula but also produces a new stability bound of a + b, which is conjectured to be sharp, and determines the exact degree of the dimension polynomial, which is also a + born
- Notes:
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- Advisors: Haglund, James Committee members: Gadish, Nir; Skandera, Mark
- Ph.D. University of Pennsylvania 2025
- Local Notes:
- School code: 0175
- ISBN:
- 9798280762152
- Access Restriction:
- Restricted for use by site license
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.