SkewFactorialSchurPol: Skew factorial Schur polynomial

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

Skew factorial Schur polynomial

Description

Computes the skew factorial Schur polynomial associated to a given skew partition.

Usage

SkewFactorialSchurPol(n, lambda, mu, a, i0)

Arguments

n	number of variables
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)
a	vector of bigq numbers, or vector of elements coercible to bigq numbers; this vector corresponds to the sequence denoted by a in the reference paper, section 6th Variation (in this paper a is a doubly infinite sequence, but only a finite number of indices are not involved); the length of this vector must be large enough (an error will be thrown if it is too small) but it is not easy to know the minimal possible length
i0	positive integer, the index of a that must be considered as the zero index of the sequence denoted by a in the reference paper

Value

A qspray polynomial.

References

I.G. Macdonald. Schur functions: theme and variations. Publ. IRMA Strasbourg, 1992.

Examples

# for a=c(0, 0, ...), the skew factorial Schur polynomial is the
# skew Schur polynomial; let's check
n <- 4
lambda <- c(3, 3, 2, 2); mu <- c(2, 2)
a <- rep(0, 9)
i0 <- 3
skewFactorialSchurPoly <- SkewFactorialSchurPol(n, lambda, mu, a, i0)
skewSchurPoly <- SkewSchurPol(n, lambda, mu)
skewFactorialSchurPoly == skewSchurPoly # should be TRUE

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