KostkaJackNumbers: Kostka-Jack numbers with a given Jack parameter
Description
Kostka numbers with Jack parameter, or Kostka-Jack numbers,
for partitions of a given weight and a given Jack parameter.
Usage
KostkaJackNumbers(n, alpha = "1")
Value
The matrix of the Kostka-Jack numbers \(K_{\lambda,\mu}(\alpha)\)
given as character strings representing integers or fractions.
The row names of this matrix encode the partitions \(\lambda\) and
the column names encode the partitions \(\mu\)
Arguments
n
positive integer, the weight of the partitions
alpha
the Jack parameter, a bigq number or an object coercible
to a bigq number
Details
The Kostka-Jack number \(K_{\lambda,\mu}(\alpha)\) is the
coefficient of the monomial symmetric polynomial \(m_\mu\) in the
expression of the \(P\)-Jack polynomial \(P_\lambda(\alpha)\) as a
linear combination of monomial symmetric polynomials. For \(\alpha=1\)
it is the ordinary Kostka number.