On computing Schur functions and series thereof
Tóm tắt
In this paper, we present two new algorithms for computing all Schur functions
$$s_\kappa (x_1,\ldots ,x_n)$$
for partitions
$$\kappa $$
such that
$$|\kappa |\le N$$
. For nonnegative arguments,
$$x_1,\ldots ,x_n$$
, 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
$$\mathscr {O}(n^2)$$
.
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