Bowman, Chris, Paget, Rowena (2023) The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture. Journal of Algebra, 655 . pp. 110-138. ISSN 0021-8693. E-ISSN 1090-266X. (doi:10.1016/j.jalgebra.2023.08.042) (KAR id:102689)
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| Official URL: https://doi.org/10.1016/j.jalgebra.2023.08.042 |
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Abstract
We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This provides an explanation of the stability properties of plethysm and Kronecker coefficients in a simple and uniform fashion for the first time. We prove the strengthened Foulkes' conjecture for stable coefficients in an elementary fashion.
| Item Type: | Article |
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| DOI/Identification number: | 10.1016/j.jalgebra.2023.08.042 |
| Uncontrolled keywords: | Symmetric groups; Plethysm coefficients; Schur-Weyl duality; Partition algebras |
| Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory |
| Institutional Unit: | Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences |
| Former Institutional Unit: |
Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
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| Funders: | University of Kent (https://ror.org/00xkeyj56) |
| Depositing User: | Rowena Paget |
| Date Deposited: | 05 Sep 2023 11:28 UTC |
| Last Modified: | 03 Nov 2025 21:50 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/102689 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Paget, Rowena.
| Creator's ORCID: |
 https://orcid.org/0000-0001-8088-4421
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