Abstract
This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to give a heuristic procedure to check realisability. In particular we disprove Matheron's conjecture, and explicit partially the structure of the convex body formed by realisable unit covariances in a finite set.
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