14,502 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 $\mathbb{F}_{q}$ be a finite field, $\mathbb{F}_{q^s}$ be an extension of
$\mathbb{F}_q$, let $f(x)\in \mathbb{F}_q[x]$ be a polynomial of degree $n$
with $\gcd(n,q)=1$. We present a recursive formula for evaluating the
exponential sum $\sum_{c\in \mathbb{F}_{q^s}}\chi^{(s)}(f(x))$. Let $a$ and $b$
be two elements in $\mathbb{F}_q$ with $a\neq 0$, $u$ be a positive integer. We
obtain an estimate for the exponential sum $\sum_{c\in
\mathbb{F}^*_{q^s}}\chi^{(s)}(ac^u+bc^{-1})$, where $\chi^{(s)}$ is the lifting
of an additive character $\chi$ of $\mathbb{F}_q$. 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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