An Asymptotic Isoperimetric Inequality

Abstract. For a finite metric space V with a metric $ \rho $, let V n be the metric space in which the distance between (a1, . . ., an) and (b1, . . ., bn) is the sum $ \sum^{n}_{i = 1} \rho (a_i, b_i) $. We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V n of distance at least d from a set of half the points of V n, when n tends to infinity and d satisfies $ d \gg \sqrt {n} $.

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