Expression of a skew Schur polynomial as a linear combination of Schur polynomials.
LRskew(lambda, mu, output = "dataframe")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.
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)
the type of the output, "dataframe" or "list"
library(jack)
LRskew(lambda = c(4, 2, 1), mu = c(3, 1))
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