Permutation polytopes corresponding to strongly supermodular functions
Throughout, let p be a positive integer and let ? be the set of permutations over {1,,p}. A real-valued function ? over subsets of {1,,p}, with ?(?)=0, defines a mapping of ? into where ??? is mapped into the vector ?? whose kth coordinate (??)k is the augmented ?-value obtained from adding k to the coordinates that precede it, according to the ranking induced by ?. The permutation polytope corresponding to ? is then the convex hull of the vectors corresponding to all permutations. We introduce a new class of strongly supermodular functions and for such functions we derive an isomorphic representation for the face-lattices of the corresponding permutation polytope.
permutations polytopes supermodularity cores of games