Integral Majorization Polytopes

Authors

Fuzhen Zhang, Nova Southeastern UniversityFollow
Geir Dahl, University of Oslo

Document Type

Article

Publication Date

9-1-2013

Publication Title

Discrete Mathematics, Algorithms and Applications

Keywords

Ferrers diagram; Integer partition; Majorization; Polytope

ISSN

1793-8309

Volume

5

Issue/No.

3

First Page

12pp

Abstract

The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a given vector a ∈ ℝn; this is a polytope with extreme points being the permutations of a. For integral vector a, let ν(a) be the number of integral vectors contained in M(a). We present several properties of the function ν and provide an algorithm for computing ν(a).

Comments

AMSC: 52B05, 05A17, 15A39

NSUWorks Citation

Zhang, Fuzhen and Dahl, Geir, "Integral Majorization Polytopes" (2013). Mathematics Faculty Articles. 67.
https://nsuworks.nova.edu/math_facarticles/67

DOI

10.1142/S1793830913500195