jacobiTrudi -- Jacobi-Trudi determinant

Synopsis

Usage:

f = jacobiTrudi(lambda,R)
Inputs:
- lambda, a basic list, a nonincreasing list of integers, or a partition
- R, a ring, a Symmetric ring
Optional inputs:
- EorH => ..., default value "E", e- or h- representation of Jacobi-Trudi determinant
- Memoize => ..., default value true, Store values of the jacobiTrudi function.
Outputs:
- f, a ring element, an element of a Symmetric ring

Description

Given a partition lambda and Symmetric ring R, the method evaluates the Jacobi-Trudi determinant corresponding to the partition lambda, yielding a representation of the Schur function s_{lambda} as a symmetric function in R. The default option is to represent this symmetric function in terms of e-polynomials.

i1 : R = symmetricRing(QQ,10);

i2 : jacobiTrudi({3,2,2,1},R)

               2
o2 = e e e  - e  - e e e  + e e
      1 3 4    4    1 2 5    2 6

o2 : R

i3 : jacobiTrudi(new Partition from {4,4,1},R,EorH => "H")

        2
o3 = h h  - h h h  - h h  + h h
      1 4    1 3 5    4 5    3 6

o3 : R

i4 : toS oo

o4 = s
      4,4,1

o4 : schurRing (QQ, s, 10)

Ways to use jacobiTrudi :

jacobiTrudi(BasicList,Ring)

For the programmer

The object jacobiTrudi is a method function with options.