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# Weak k-Majorization and Polyhedra

journal contribution

posted on 2010-01-01, 00:00 authored by Geir Dahl, Francois MargotFrancois MargotFor integers k and n with k ≤ n a vector x ∈ ℝ

^{n}is said to be weakly k-majorized by a vector q ∈ ℝ^{k}if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1,⋯,k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P(q; k). We determine the vertices of both P(q; k) and its integer hull Q(q; k). Furthermore a complete and nonredundant linear description of Q(q; k) is given