Hypermetrics in geometry of numbers

A nite semimetric d on a set X is hypermetric if it satisses the inequality P i;j2X b i b j d ij 0 for all b 2 Z X with P i2X b i = 1. Hypermetricity turns out to be the appropriate notion for describing the metric structure of holes in lattices. We survey hypermetrics, their connections with lattices and applications.

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