相关论文: On the center of a finite Dickson nearfield

For a Dickson pair $(q,n)$ we show that $ \big \lbrace \frac{q^k-1}{q-1}, 1 \leq k < n \big \rbrace $ forms a finite complete set of different residues modulo $n$. We also study the construction of a finite Dickson nearfield that arises…

We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras.

In this paper we collect and improve the techniques for calculating the nuclei of a semifield and we use these tools to determine the order of the nuclei and of the center of some commutative presemifields of odd characteristic recently…

We survey the classical results of the Dirichlet Approximation Theorem.

We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…

A well-known object in classical Euclidean geometry is the circumcenter of a triangle, i.e., the point that is equidistant from all vertices. The purpose of this paper is to provide a systematic study of the circumcenter of sets containing…

We study a specific family of uniformly isochronous polynomial systems. Our results permit to solve a problem about centers of such systems.

The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…

In this work, we review the concept of center of a geometric object as an equivariant map, unifying and generalizing different approaches followed by authors such as C. Kimberling or A. Edmonds. We provide examples to illustrate that this…

In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a conic.

We provide a model of the split Cayley hexagon arising from the Hermitian surface $\mathsf{H}(3,q^2)$, thereby yielding a geometric construction of the Dickson group $G_2(q)$ starting with the unitary group $\mathsf{SU}_3(q)$.

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of…

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{F}_p$. We also study the permutation…

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…

In this paper, we give explicit descriptions of the centers and cocenters of $0$-Hecke algebras associated to finite Coxeter groups.

We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.

We discuss the properties and the permutation behaviour of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ over finite fields. The results in this paper unify and generalize several recently discovered results on…

The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially…

This paper focuses on twisted affine quantum algebras: an integer form is chosen, and the center of its specialization at odd roots of 1 (of order bigger than 3 in case D_4^{(3)}, bigger than 1 otherwise) is described.