Related papers: Degenerate binomial and degenerate Poisson random …
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $3$-dimensional Poisson algebras. In addition, we study the…
The nth r-extended Lah-Bell number is defined as the number of ways a set with $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to…
In this paper, we consider the degenerate Daehee numbers and polynomials of the second kind which are different from the previously introduced Daehee numbers and polynomials. We investigate some properties of these numbers and polynomials.…
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha, \beta}(\lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that…
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…
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…
Many important special numbers appear in the expansions of some polynomials in terms of central factorials and vice versa, for example central factorial numbers, degenerate central factorial numbers, and central Lah numbers which are…
The aim of this paper is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential…
Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the…
Recently, Freud-Rodriguez proposed a new counting process which is called the Bell-Touchard process and based on the Bell-Touchard probability distribution. This process was developed to solve the problem of rare events hypothesis which is…
We study $q$-deformation of probability measures on partitions, i.e., $q$-deformed random partitions. We in particular consider the $q$-Plancherel measure and show a determinantal formula for the correlation function using a $q$-deformation…
Recently, the degenerate harmonic and the degenerate hyperharmonic numbers are introduced respectively as degenerate versions of the harmonic and the hyperharmonic numbers. The aim of this paper is to introduce the degenerate…
This paper addresses the unnatural appearance of the two-variable degenerate Fubini polynomials in a recently derived Spivey-type recurrence relation for the fully degenerate Bell polynomials. To solve this, we introduce a new family of…
The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties.…
In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials…
Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the introduction of the degenerate Bernoulli and degenerate Euler polynomials by Carlitz. The aim…
We introduce a two-parameter deformation of the classical Poisson distribution from the viewpoint of noncommutative probability theory, by defining a $(q,t)$-Poisson type operator (random variable) on the $(q,t)$-Fock space \cite{Bl12} (See…
Consider a second-order elliptic operator $L$ in the half-plane $\mathbb R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ is used in the representation of positive $L$-harmonic…
In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell…
In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincar\'e residue of a meromorphic volume…