jack (version 6.0.0)

LRmult: Littlewood-Richardson rule for multiplication

Description

Expression of the product of two Schur polynomials as a linear combination of Schur polynomials.

Usage

LRmult(mu, nu, output = "dataframe")

Value

This computes the expression of the two Schur polynomials associated to mu and nu 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 lambda 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 lambda is the list of partitions defining the Schur polynomials of the linear combination given as integer vectors.

Arguments

mu, nu

integer partitions, given as vectors of decreasing integers

output

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

Examples

library(jack)
mu <- c(2, 1)
nu <- c(3, 2, 1)
LR <- LRmult(mu, nu, output = "list")
LRcoeffs <- LR$coeff
LRparts <- LR$lambda
LRterms <- lapply(1:length(LRcoeffs), function(i) {
  LRcoeffs[i] * SchurPol(3, LRparts[[i]])
})
smu_times_snu <- Reduce(`+`, LRterms)
smu_times_snu == SchurPol(3, mu) * SchurPol(3, nu)