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From: Art Werschulz on 29 Apr 2010 09:22
Hi all.

Let $\lambda_1\ge\lambda_2\ge\dots>0$. Let $d$ be a positive integer. For
a multi-index $\alpha=[\alpha_1,\dots,\alpha_d]$ of positive integers, let
$$\lambda_\alpha = \prod_{j=1}^d \lambda_{\alpha_j}.$$
Now suppose that $\lambda_{\alpha}^{(n)}$ is the $n$th-largest element in
the set $\{\lambda_\alpha: \alpha\in\mathbb N^d\}$.

Does anybody know an efficient algorithm for computing
$\lambda_\alpha^{(1)}, \lambda_\alpha^{(2)}, \dots, \lambda_\alpha^{(n)}$?
What is its running time, as a function of $n$ and $d$?

Thanks.

--
Art Werschulz (8-{)} "Metaphors be with you." -- bumper sticker
GCS/M (GAT): d? -p+ c++ l++ u+ P++ e--- m* s n+ h f g+ w+ t+ r-
Internet: agw STRUDEL cs.columbia.edu
ATTnet: Columbia U. (646) 775-6035, Fordham U. (212) 636-6325
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