14,761 research outputs found
Partitions of the polytope of Doubly Substochastic Matrices
In this paper, we provide three different ways to partition the polytope of
doubly substochastic matrices into subpolytopes via the prescribed row and
column sums, the sum of all elements and the sub-defect respectively. Then we
characterize the extreme points of each type of convex subpolytopes. The
relations of the extreme points of the subpolytopes in the three partitions are
also given
On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields
Let be a finite field, be an extension of
, let be a polynomial of degree
with . We present a recursive formula for evaluating the
exponential sum . Let and
be two elements in with , be a positive integer. We
obtain an estimate for the exponential sum , where is the lifting
of an additive character of . Some properties of the
sequences constructed from these exponential sums are provided also.Comment: 18 page
On the maximum of the permanent of (I-A)
Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum
of all elements of A. In this paper we give the upper bound of the permanent of
(I-A) with respect to n and {\sigma}(A)
Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices
We investigate convex polytopes of doubly stochastic matrices having special
structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric
and Hankel symmetric. We determine dimensions of these polytopes and classify
their extreme points. We also determine a basis of the real vector spaces
generated by permutation matrices with these special structures
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