Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777432 | European Journal of Combinatorics | 2017 | 5 Pages |
Abstract
Let JTλ be the Jacobi-Trudi matrix corresponding to the partition λ, so detJTλ is the Schur function sλ in the variables x1,x2,â¦. Set x1=â¯=xn=1 and all other xi=0. Then the entries of JTλ become polynomials in n of the form (n+jâ1j). We determine the Smith normal form over the ring Q[n] of this specialization of JTλ. The proof carries over to the specialization xi=qiâ1 for 1â¤iâ¤n and xi=0 for i>n, where we set qn=y and work over the ring Q(q)[y].
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Richard P. Stanley,