KostkaJackNumbers: Kostka-Jack numbers with a given Jack parameter

In jack: Jack, Zonal, Schur, and Other Symmetric Polynomials

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 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)

jack documentation built on Sept. 11, 2024, 6:34 p.m.