On computing Schur functions and series thereof

Abstract

Abstract In this paper, we present two new algorithms for computing all Schur functions

$$s_\kappa (x_1,\ldots ,x_n)$$

s κ

(

x 1

, … ,

x n

)

for partitions

$$\kappa $$

κ

such that

$$|\kappa |\le N$$

| κ | ≤ N

. For nonnegative arguments,

$$x_1,\ldots ,x_n$$

x 1

, … ,

x n

, 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

$$\mathscr {O}(n^2)$$

O (

n 2

)

.