Related papers: On Two Classes of Regular Sequences
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…
We investigate small $p$-groups with cohomology rings of depth higher than predicted by Duflot's theorem. In these groups, a sampling would suggest several naive conjectures about the degrees of the additional regular sequence elements. We…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.
In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their…
Two new matrix classes are introduced; inverse cyclic matrices and bi-diagonal south-west matrices. An interesting relation is established between these classes. Applications to two classes of inverse $Z$-matrices are provided.
We study periodic linear trajectories in the double pentagon and periodic billiard trajectories in the regular pentagon.
In this paper, we consider a general form of the analogue of Ramanujan's sum in the ring of polynomials over a finite field. We first prove some multiplicative properties of such functions before considering their finite Fourier series and…
General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.
We consider three types of rings of supersymmetric polynomials: polynomial ones $\Lambda_{m,n}$, partially polynomial $\Lambda_{m,n}^{+y}$ and Laurent supersymmetric rings $\Lambda_{m,n}^{\pm}$. For each type of rings we give their…
We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…
In this note, we present a new proof that the cyclotomic integers constitute the full ring of integers in the cyclotomic field.
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.
The numerical radius of the general $2\times2$ complex matrix is calculated.
We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo $n$ and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. The second…
We classify two-variable polynomials which are rational of simple type. These are precisely the two-variable polynomials with trivial homological monodromy.
In this paper 101 new integer sequences, sub-sequences, and sequences of sequences, together with related unsolved problems and conjectures, are presented. Also, definitions, examples, solved or open questions, and references for each…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…