On computing Schur functions and series thereof

Abstract

In this paper, we present two new algorithms for computing all Schur functions sκ(x1, … , xn) for partitions κ such that | κ| ≤ N. For nonnegative arguments, x1, … , xn, both algorithms are subtraction-free and thus each Schur function is computed to high relative accuracy in floating point arithmetic. The cost of each algorithm per Schur function is O(n2).