Related papers: Multiplier Sequences for Generalized Laguerre Base…
In this paper we introduce three combinatorial models for symmetrized poly-Bernoulli numbers. Based on our models we derive generalizations of some identities for poly-Bernoulli numbers. Finally, we set open questions and directions of…
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…
We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…
We use the methods of empirical mathematics to show that iterative logarithmic operations will result in an attractor point on the complex plane. Moreover, we demonstrate that different bases converge onto different attractors. Finally, we…
This paper surveys and illustrates geometric methods for constructing normal bases allowing efficient finite field arithmetic. These bases are constructed using the additive group, the multiplicative group and the Lucas torus. We describe…
The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More precisely, in such cases, the image of a multilinear…
Legendre's relation for the complete elliptic integrals of the first and second kinds is generalized. The proof depends on an application of the generalized trigonometric functions and is alternative to the proof for Elliott's identity.
Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval Gabor single-frame or multi-frame generators. An interesting and natural question is how to characterize all such…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons.…
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…
The classical De Jonquieres and MacDonald formulas describe the virtual number of divisors with prescribed multiplicities in a linear system on an algebraic curve. We establish an essentially optimal result concerning the enumerative…
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a…