On Computing Schur Functions and Series Thereof

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 ) .