Related papers: Probabilistic derangement numbers and polynomials
We use a probabilistic approach to describe the behavior as $n -> \infty$ of the Laplace transforms of $P^n$, where $P$ a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer in the…
The zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers, which are also known as the conditional Poisson distributions or the positive Poisson distributions. In…
In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
Recently, introduced are the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials. The aim of this note is to study the multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials which are defined by…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
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…
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were recently introduced by Jang et. al. We derive their explicit expressions and some…
Building on the work of Arizmendi and Celestino (2021), we derive the $*$-distributions of polynomials in monotone independent and infinitesimally monotone independent elements. For non-zero complex numbers $\alpha$ and $\beta$, we derive…
In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.
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…
Recently, the $\lambda$-analogues of $r$-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the $\lambda$-analogues of $r$-Stirling numbers of the second kind and to investigate some…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
In this paper we study bounds for the total variation distance between two second degree polynomials in normal random variables provided that they essentially depend on at least three variables.
Recently, several types of degenerate Bell polynomials have been introduced as degenerate versions of the ordinary Bell polynomials. The aim of this paper is to study some identities for the degenerate Bell polynomials and their related…