The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

A transportation polytope consists of all multidimensional arrays or tables of non-negative
real numbers that satisfy certain sum conditions on subsets of the entries. They arise …

The geometry of the compact convex set of all n× n doubly stochastic matrices, a structure
frequently referred to as the Birkhoff polytope, has been an active subject of research as of …

Although they play a fundamental role in nearly all branches of mathematics, inequalities
are usually obtained by ad hoc methods rather than as consequences of some underlying …

Let article mathrsfs amsmath, amssymb empty n be the compact convex set of tridiagonal
doubly stochastic matrices. These arise naturally in probability problems as birth and death …

An alternating sign matrix, or ASM, is a (0,±1)-matrix where the nonzero entries in each row
and column alternate in sign, and where each row and column sum is 1. We study the …

An n× n real matrix (not necessarily nonnegative) A is g-doubly stochastic (generalized
doubly stochastic) if all its row and column sums are one. The sets of all g-doubly stochastic …

The diameter of the acyclic Birkhoff polytope Page 1 Linear Algebra and its Applications 428
(2008) 1524–1537 Available online at www.sciencedirect.com www.elsevier.com/locate/laa …

The fractional perfect b-matching polytope of an undirected graph G is the polytope of all
assignments of nonnegative real numbers to the edges of G such that the sum of the …

In linear optimization we are considering problems that can be presented as linear
programming problems, which will be defined in chapter 2. The topic of this thesis will be the …