Integral Majorization Polytopes

Fuzhen Zhang; Geir Dahl

doi:10.1142/S1793830913500195

Integral Majorization Polytopes

Fuzhen Zhang
, Geir Dahl

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

<p> The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a given vector a ∈ &reals;n; 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).</p>

Original language	American English
Journal	Discrete Mathematics, Algorithms and Applications
Volume	5
DOIs	https://doi.org/10.1142/S1793830913500195
State	Published - Sep 1 2013

Keywords

Ferrers diagram; Integer partition; Majorization; Polytope

Disciplines

Mathematics

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title = "Integral Majorization Polytopes",

abstract = " The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a given vector a \∈ \&reals;n; 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).",

keywords = "Ferrers diagram; Integer partition; Majorization; Polytope",

author = "Fuzhen Zhang and Geir Dahl",

year = "2013",

month = sep,

day = "1",

doi = "10.1142/S1793830913500195",

language = "American English",

volume = "5",

journal = "Discrete Mathematics, Algorithms and Applications",

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publisher = "World Scientific",

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T1 - Integral Majorization Polytopes

AU - Zhang, Fuzhen

AU - Dahl, Geir

PY - 2013/9/1

Y1 - 2013/9/1

N2 - The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a given vector a ∈ &reals;n; 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).

AB - The majorization polytope M(a) consists of all vectors dominated (or majorized, to be precise) by a given vector a ∈ &reals;n; 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).

KW - Ferrers diagram; Integer partition; Majorization; Polytope

UR - https://nsuworks.nova.edu/math_facarticles/67

U2 - 10.1142/S1793830913500195

DO - 10.1142/S1793830913500195

M3 - Article

SN - 1793-8309

VL - 5

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

ER -

Integral Majorization Polytopes

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