Re: Multisets of integers with equal sums, sums-of-squares, etc.

In article <ftaqa4$cq5$1@xxxxxxxxxxxxxxxx>,
"joeshipman@xxxxxxx" <JoeShipman@xxxxxxx> wrote:

The multisets {3,3} and {1,1,4} have equal sums and equal sums-of-
squares. What's the smallest example of two multisets of integers
which have the same sums-of-nth-powers for n=1,2,3? What's the
smallest example for n=1,2,3,4?

I am interested in this because multisets with equal sums and sums-of-
squares have the same mean and standard deviation. Sampling with
replacement from these multisets ought to converge to the same thing
by the Central Limit Theorem, but I want to illustrate how the rate of
convergence depends on higher moments, using examples that are
numerically simple.

This is the Tarry-Escott problem, q.v., no?

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)

.

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