| KostkaJackNumbers {jack} | R Documentation |
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")
Arguments
n |
positive integer, the weight of the partitions |
alpha |
the Jack parameter, a |
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.
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
See Also
KostkaJackNumbersWithGivenLambda,
symbolicKostkaJackNumbers,
skewKostkaJackNumbers.
Examples
KostkaJackNumbers(4)