منابع مشابه
MONOTONICTTY CONJECTURE ON PERMANENTS OF DOUBLY STOCHASTIC MATRICES i
A stronger version of the van der Waerden permanent conjecture asserts that if J„ denotes the n X n matrix all of whose entries are \/n and A is any fixed matrix on the boundary of the set ofnxn doubly stochastic matrices, then per(A/4 + (1 — \)Jn) as a function of X is nondecreasing in the interval [0, 1]. In this paper, we elucidate the relation of this assertion to some other conjectures kno...
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In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices I...
متن کاملMinimum permanents on two faces of the polytope of doubly stochastic matrices∗
We consider the minimum permanents and minimising matrices on the faces of the polytope of doubly stochastic matrices whose nonzero entries coincide with those of, respectively, Um,n = [ In Jn,m Jm,n 0m ] and Vm,n = [ In Jn,m Jm,n Jm,m ] . We conjecture that Vm,n is cohesive but not barycentric for 1 < n < m + √ m and that it is not cohesive for n > m + √ m. We prove that it is cohesive for 1 <...
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Doubly stochastic measures can be identi ed with the trace of a pair of (Lebesgue) measure preserving maps of the unit interval to itself. It has been of traditional interest in probability theory to produce a random vector (or metric space element), which has a given distribution and is de ned on a standard space, such as [0; 1] endowed with Lebesgue measure. In a classic work, L evy [4, secti...
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Given an n-vertex graph G, the matrix Ω(G) = (In + L(G))−1 = (ωij) is called the doubly stochastic graph matrix of G, where In is the n × n identity matrix and L(G) is the Laplacian matrix of G. Let ω(G) be the smallest element of Ω(G). Zhang and Wu [X.D. Zhang and J.X. Wu. Doubly stochastic matrices of trees. Appl. Math. Lett., 18:339–343, 2005.] determined the tree T with the minimum ω(T ) am...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00367-7