%0 Journal Article
%T Core-based criterion for extreme supermodular functions
%A M. Studeny
%A T. Kroupa
%J Mathematics
%D 2014
%I arXiv
%X We give a necessary and sufficient condition for extremality of a supermodular function based on its min-representation by means of (vertices of) the corresponding core polytope. The condition leads to solving a certain simple linear equation system determined by the combinatorial core structure. Our result allows us to characterize indecomposability in the class of generalized permutohedra. We provide an in-depth comparison between our result and the description of extremality in the supermodular/submodular cone achieved by other researchers.
%U http://arxiv.org/abs/1410.8395v1