Restriction coefficients for partitions with at most three columns
Abstract
Let r ≥ 0 , and let λ and μ be partitions such that λ 1 ≤ r + 1 . We present a combinatorial interpretation of the plethysm coefficient 〈 s λ , s μ [ s r ] 〉 . As a consequence, we solve the restriction problem for partitions with at most three columns. That is, for all partitions λ with λ 1 ≤ 3 , we find a combinatorial interpretation for the multiplicities of the irreducible 𝔖 n -submodules of the Schur module 𝕊 λ ℂ n , considered as an 𝔖 n -module.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Functional Equations Stability Results
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 9
- Issue
- 2
- Pages
- 543–555
- Publication date
- 30 April 2026
- Language
- EN