syt (version 0.5.0)

KostkaNumber: Kostka number

Description

Computes a Kostka number.

Usage

KostkaNumber(lambda, mu)

Value

The Kostka number corresponding to lambda and mu.

Arguments

lambda

an integer partition

mu

an integer vector whose sum equals the weight (i.e. the sum) of lambda

Details

The Kostka number \(K(\lambda,\mu)\) is the number of semistandard Young tableaux with shape \(\lambda\) and weight \(\mu\). It does not depend on the order of the elements of \(\mu\) (so one can always take an integer partition for \(\mu\)). The weight is the vector whose \(i\)-th element is the number of occurrences of \(i\) in the tableau.

See Also

KostkaNumbers, KostkaNumbersWithGivenMu, KostkaNumbersWithGivenLambda, skewKostkaNumbers.

Examples

KostkaNumber(c(3,2), c(1,1,1,2))
KostkaNumber(c(3,2), c(1,1,2,1))
KostkaNumber(c(3,2), c(1,2,1,1))
KostkaNumber(c(3,2), c(2,1,1,1))
lambda <- c(4, 3, 1)
mu <- rep(1, sum(lambda))
KostkaNumber(lambda, mu) == count_sytx(lambda) # should be TRUE