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 bigq number or an object coercible to a bigq number

Details

The Kostka-Jack number Kλ,μ(α)K_{\lambda,\mu}(\alpha) is the coefficient of the monomial symmetric polynomial mμm_\mu in the expression of the PP-Jack polynomial Pλ(α)P_\lambda(\alpha) as a linear combination of monomial symmetric polynomials. For α=1\alpha=1 it is the ordinary Kostka number.

Value

The matrix of the Kostka-Jack numbers Kλ,μ(α)K_{\lambda,\mu}(\alpha) given as character strings representing integers or fractions. The row names of this matrix encode the partitions λ\lambda and the column names encode the partitions μ\mu

See Also

KostkaJackNumbersWithGivenLambda, symbolicKostkaJackNumbers, skewKostkaJackNumbers.

Examples

KostkaJackNumbers(4)

[Package jack version 6.1.0 Index]