skewKostkaNumbers {syt}

Skew Kostka numbers

Description

Skew Kostka numbers associated to a given skew partition.

Usage

skewKostkaNumbers(lambda, mu, output = "vector")

Arguments

lambda, mu

integer partitions defining the skew partition: lambda is the outer partition and mu is the inner partition (so mu must be a subpartition of lambda)

output

the format of the output, either "vector" or "list"

Details

The skew Kostka number K_{\lambda/\mu,\nu} is the number of skew semistandard Young tableaux with shape \lambda/\mu and weight \nu. The weight of a Young tableau is the vector whose i-th element is the number of occurrences of i in this tableau.

Value

If output="vector", the function returns a named vector. This vector is made of the positive skew Kostka numbers K_{\lambda/\mu,\nu} and its names encode the partitions \nu. If ouput="list", the function returns a list. Each element of this list is a named list with two elements: an integer partition \nu in the field named "nu", and the corresponding skew Kostka number K_{\lambda/\mu,\nu} in the field named "value". Only the non-null skew Kostka numbers are provided by this list.

See Also

KostkaNumber, KostkaNumbersWithGivenMu.

Examples

skewKostkaNumbers(c(4,2,2), c(2,2))