1. What are the contributions in this paper?
In this paper the authors study majorization polytopes for more general integral vectors.
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Integral majorization polytopes
Geir Dahl,Fuzhen Zhang +1 more
TL;DR: This work presents several properties of the function ν and provides an algorithm for computing ν(a), the number of integral vectors contained in majorization polytope M(a).
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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).
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Citations
The Laplacian energy of threshold graphs and majorization
TL;DR: In this paper, the Laplacian energy of threshold graphs is analyzed using Ferrers diagrams and ideas from majorization theory, and new inequalities for threshold degree sequences are obtained in this process.
12
A note on majorization transforms and Ryser’s algorithm
TL;DR: A new type of majorization transfer called L-transforms is introduced and some of its properties are proved and discussed how it gives a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.
References
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Inequalities: Theory of Majorization and Its Applications
Albert W. Marshall,Ingram Olkin,Barry C. Arnold +2 more
- 06 Apr 2011
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
7K
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Lectures on Polytopes
Günter M. Ziegler
- 29 Nov 1994
TL;DR: In this article, the authors present a rich collection of material on the modern theory of convex polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids).
3.8K
•Book
Enumerative Combinatorics
Charalambos A. Charalambides
- 01 Jan 2002
TL;DR: This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
3.1K
•Book
Matrix Theory: Basic Results and Techniques
Fuzhen Zhang
- 27 May 1999
TL;DR: In this paper, the authors present an elementary linear algebra review of the second edition of the Second Edition of the Basic Linear Algebra (BLA) and discuss the use of matrix polynomials and Canonical forms.
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