Strong greedoid structure of r-removed P-orderings

Inspired by the notion of r-removed P-orderings introduced in the setting of Dedekind domains by Bhargava we generalize it to the framework of arbitrary ultrametric spaces. We show that sets of maximal ”r-removed perimeter” can be constructed by a greedy algorithm and form a strong greedoid. This gives a simplified proof of several theorems previously obtained by Bhargava, as well as generalises some results of Grinberg and Petrov who considered the case r = 0 corresponding, in turn, to simple P-orderings.