jack (version 6.0.0)

LRskew: Littlewood-Richardson rule for skew Schur polynomial

Description

Expression of a skew Schur polynomial as a linear combination of Schur polynomials.

Usage

LRskew(lambda, mu, output = "dataframe")

Value

This computes the expression of the skew Schur polynomial associated to the skew partition defined by lambda and mu

as a linear combination of Schur polynomials. If output="dataframe", the output is a dataframe with two columns: the column coeff gives the coefficients of this linear combination, and the column nu

gives the partitions defining the Schur polynomials of this linear combination as character strings, e.g. the partition c(4, 3, 1) is given by "4, 3, 1". If output="list", the output is a list with two fields: the field coeff is the vector made of the coefficients of the linear combination, and the field nu is the list of partitions defining the Schur polynomials of the linear combination given as integer vectors.

Arguments

lambda, mu

integer partitions defining the skew partition: lambda is the outer partition and mu is the inner partition (so mu must be a subpartition of lambda)

output

the type of the output, "dataframe" or "list"

Examples

library(jack)
LRskew(lambda = c(4, 2, 1), mu = c(3, 1))