Every Finite Distributive Lattice Is Isomorphic To The Minimizer Set Of An M-#-Concave Set Function

M-#-concavity is a key concept in discrete convex analysis. For set functions, the class of M-#-concavity is a proper subclass of submodularity. It is a well-known fact that the set of minimizers of a submodular function forms a distributive lattice, where every finite distributive lattice is possible to appear. It is a natural question whether every finite distributive lattice appears as the minimizer set of an M-#-concave set function. This paper affirmatively answers the question. (c) 2020 Elsevier B.V. All rights reserved.