Related papers: Higher Order r-Dowling polynomials
We address a systematic combinatorial approach to the anti-normal ordering problem. In this way, we use the Stirling numbers and their generating function, the so-called Bell polynomials, together with the operational methods to anti-normal…
In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.
Preorder polytopes, defined from preorders on finite sets, are introduced and studied from a lattice point enumeration point of view. They naturally generalize arbor polytopes, recently introduced and studied by the second named author.…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
It is well known that the Bell numbers represent the total number of partitions of an n-set. Similarly, the Stirling numbers of the second kind, represent the number of k-partitions of an n-set. In this paper we introduce a certain…
Following the ideas of L. Carlitz we introduce a generalization of the Bernoulli and Eulerian polynomials of higher order to vectorial index and argument. These polynomials are used for computation of the vector partition function $W({\bf…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
It is well known that ascents, descents and plateaux are equidistributed over the set of classical Stirling permutations. Their common enumerative polynomials are the second-order Eulerian polynomials, which have been extensively studied by…
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that appears to be relevant to the so-called Boson normal ordering problem. They provided a…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
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…
In this paper, certain mixed special polynomial families associated with Appell sequences are introduced and their properties are established. Further, operational rules providing connections between these families and the known special…
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…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
We introduce multinomial and $r$-variants of several classic objects of combinatorial probability, such as the random recursive and Hoppe trees, random set partitions and compositions, the Chinese restaurant process, Feller's coupling, and…
Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via…
Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and…
The aim of this paper is to study some basic properties of the r$-extended Lah-Bell numbers and polynomials associated with r-Lah numbers and to show the connection between the r-extended Lah-Bell polynomials and the rising factorial…