Related papers: Pisot numbers, Salem numbers, and generalised poly…
Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a given size of an infinite sequence. How practical is this…
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized $m$-gonal numbers required…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number $\alpha$ such that $\Q[\alpha] = \F$ given a real Galois extension $\F$ of $\Q$ by its integral…
Hayes equivalence is defined on monic polynomials over a finite field $\fq$ in terms of the prescribed leading coefficients and the residue classes modulo a given monic polynomial $Q$. We study the distribution of the number of zeros in a…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
Years ago, Zeev Rudnick defined the Poisson generic real numbers by counting the number of occurrences of long blocks of digits in the initial segments of the expansions of the real numbers in a fixed integer base. Peres and Weiss proved…
The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called {\em generalized Weyl algebras}) that are determined by two ring endomorphisms rather than one as in the case of `old'…
In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds…
We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type $B$ analogues are shown to have only real roots.…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…
Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type…
Let $\mathbb{K}$ be a number field of degree $n$ over $\mathbb{Q}$. Let $\widehat{\mathbb{A}}$ be the set of integers of $\mathbb{K}$ which are primitive over $\mathbb{Q}$ and $I(\mathbb{K})$ be its index. Gunji and McQuillan defined the…
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These…
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer and generalize linearized polynomial rings over finite fields, group rings or…