Kostka numbers with Jack parameter, or Kostka-Jack numbers \(K_{\lambda,\mu}(\alpha)\) for a given Jack parameter \(\alpha\) and a given integer partition \(\lambda\).
KostkaJackNumbersWithGivenLambda(lambda, alpha, output = "vector")If output="vector", this function returns a named vector.
This vector is made of the non-zero (i.e. positive) Kostka-Jack numbers
\(K_{\lambda,\mu}(\alpha)\) given as character strings and its names
encode the partitions \(\mu\).
If ouput="list", this function returns a list of lists.
Each of these lists has two
elements. The first one is named mu and is an integer
partition, and the second one is named value and is a bigq
rational number, the Kostka-Jack number \(K_{\lambda,\mu}(\alpha)\).
integer partition
the Jack parameter, a bigq number or anything coercible
to a bigq number
the format of the output, either "vector" or
"list"
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.
KostkaJackNumbers,
symbolicKostkaJackNumbersWithGivenLambda.
KostkaJackNumbersWithGivenLambda(c(3, 2), alpha = "2")
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