jack (version 6.1.0)

factorialSchurPol: Factorial Schur polynomial

Description

Computes a factorial Schur polynomial.

Usage

factorialSchurPol(n, lambda, a)

Value

A qspray polynomial.

Arguments

n

number of variables

lambda

integer partition

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 in the case of a non-skew partition, the non-positive indices of this sequence 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

References

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

Examples

# for a=c(0, 0, ...), the factorial Schur polynomial is the Schur polynomial
n <- 3
lambda <- c(2, 2, 2)
a <- c(0, 0, 0, 0)
factorialSchurPoly <- factorialSchurPol(n, lambda, a)
schurPoly <- SchurPol(n, lambda)
factorialSchurPoly == schurPoly # should be TRUE