| KostkaNumber {syt} | R Documentation |
Kostka number
Description
Computes a Kostka number.
Usage
KostkaNumber(lambda, mu)
Arguments
lambda |
an integer partition |
mu |
an integer vector whose sum equals the weight (i.e. the sum) of
|
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.
Value
The Kostka number corresponding to lambda and mu.
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
[Package syt version 0.5.0 Index]