LRskew {jack}

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")

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"

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. Every coefficient of this linear combination is a positive integer, a so-called Littlewood-Richardson coefficient. 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 of lists with two elements. Each of these lists with two elements corresponds to a term of the linear combination: the first element, named coeff, is the coefficient, namely the Littlewood-Richardson coefficient c^{\lambda}_{\mu,\nu}, where \nu is the integer partition given in the second element of the list, named nu, which defines the Schur polynomial of the linear combination.

Examples

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