MathDB

Let

X =\{x_0, x_1,\ldots , x_n\}

be the basis set of a finite metric space, where the points are inductively listed such that

x_k

maximizes the product of the distances from the points

\{x_0, x_1,\ldots , x_{k-1}\}

for each

1\leqslant k\leqslant n.

Prove that if for each

x\in X

we let

\Pi_x

be the product of the distances from

x{}

to every other point, then

\Pi_{x_n}\leqslant 2^{n-1}\Pi_x

for any

x\in X.

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