Geodesic
Nilpotent operators and discretely concave functions
Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 1-15

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Given a pair of submodules of a module over a discrete valuation ring, we construct a function of two integer variables. We show that this function is discretely concave and, conversely, every discretely concave function of two integer variables arises in this way. 
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V. I. Danilov; G. A. Koshevoy. Nilpotent operators and discretely concave functions. Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/IM2_2003_67_1_a0/