Abstract
Throughout, let p be a positive integer and let Σ be the set of permutations over {1,…, p}. A real-valued function λ over subsets of {1,…, p}, with λ(∅)=0, defines a mapping of Σ into R p where σ∈ Σ is mapped into the vector λ σ whose kth coordinate ( λ σ ) k is the augmented λ-value obtained from adding k to the coordinates that precede it, according to the ranking induced by σ. The permutation polytope corresponding to λ 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.
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