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Related papers: Lah-Bell numbers and polynomials

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Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…

Number Theory · Mathematics 2026-01-16 Taekyun Kim , Dae San Kim

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.

Number Theory · Mathematics 2010-08-10 Zhi-Wei Sun , Don Zagier

In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.

Number Theory · Mathematics 2015-06-16 Taekyun Kim , Dae San Kim , Hyuck-In Kwon

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…

Number Theory · Mathematics 2017-06-30 Taekyun Kim , Dae San Kim

In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is called the nth derangement number. Recently, the degenerate…

Number Theory · Mathematics 2024-10-15 Taekyun Kim , Dae San Kim

It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate…

Number Theory · Mathematics 2023-05-09 Taekyun Kim , Dae San Kim , Hye Kyung Kim

In this paper, we show that the r-Stirling numbers of both kinds, the r-Whitney numbers of both kinds, the r-Lah numbers and the r-Whitney-Lah numbers form particular cases of family of polynomials forming a generalization of the partial…

Combinatorics · Mathematics 2013-08-06 Miloud Mihoubi , mourad Rahmani

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…

Number Theory · Mathematics 2022-12-13 Taekyun Kim , Dae San Kim , Jongkyum Kwon

We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…

Combinatorics · Mathematics 2016-11-02 Hacene Belbachir , Imad Eddine Bousbaa

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials

Number Theory · Mathematics 2015-06-11 Dae San Kim , Taekyun Kim

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae…

Number Theory · Mathematics 2020-12-14 Taekyun Kim , Dae San Kim , Jongkyum Kwon , Hyunseok Lee

In this paper, we consider the degenerate Changhee numbers and polynomials of the second kind which are different from the previously introduced degenerate Changhee numbers and polynomials by Kwon-Kim-Seo (see [11]). We investigate some…

Number Theory · Mathematics 2017-08-01 Taekyun Kim , Dae San Kim

In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…

Combinatorics · Mathematics 2012-07-03 Tingyao Xiong , Hung-ping Tsao , Jonathan I. Hall

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…

General Mathematics · Mathematics 2021-03-15 Paolo Emilio Ricci

In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…

Number Theory · Mathematics 2018-11-06 Taekyun Kim , Dae San Kim , Gwan-Woo Jang

In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim , Hyuck-In Kwon , Jong-Jin Seo

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.…

Number Theory · Mathematics 2024-12-05 Taekyun Kim , Dae san Kim

We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also. The proofs are based on several series…

Combinatorics · Mathematics 2021-03-30 Khristo N. Boyadzhiev

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…

Classical Analysis and ODEs · Mathematics 2010-02-06 Donal F. Connon

In recent years, some degenerate versions of quite a few special numbers and polynomials are introduced and investigated by means of various methods. The aim of this paper is to study some results on degenerate harmonic numbers, degenerate…

Number Theory · Mathematics 2022-08-30 Taekyun Kim , Dae San Kim