Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776926 | Discrete Mathematics | 2017 | 11 Pages |
Abstract
We consider here the algebra of noncommutative symmetric functions, and two of its bases, the ribbon basis and the immaculate basis. Although a simple combinatorial formula is known for expanding an element of the ribbon basis in the immaculate basis, the reverse is not known. Using a sign-reversing involution, we prove an analogue of the classical Jacobi-Trudi formula which is an expression for an immaculate function indexed by a rectangle in the ribbon basis. We generalize this result to immaculate functions indexed by products of rectangles, and use this to prove a combinatorial formula for immaculate functions indexed by a rectangle of the form (2n).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
John M. Campbell,