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, de7nes a mapping of into R 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. c © 2003 Elsevier B.V. All rights reserved.