
This paper uses exponential sum methods to show that if
In this paper, we introduce a generalized family of numbers and polynomials of one or more variables attached to the formal composition
In this paper, we show that the generalized exponential polynomials and the generalized Fubini polynomials satisfy certain binomial identities and that these identities characterize the mentioned polynomials (up to an affine transformation of the variable) among the class of the normalized Sheffer sequences.
Let
In this paper, we will recover the generating functions of Tribonacci numbers and Chebychev polynomials of first and second kind. By making use of the operator defined in this paper, we give some new generating functions for the binary products of Tribonacci with some remarkable numbers and polynomials. The technique used here is based on the theory of the so-called symmetric functions.
It is shown that if
Extensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these partitions are established. Connections with Riordan arrays are presented.
Every set of natural numbers determines a generating function convergent for
We prove some combinatorial identities by an analytic method. We use the property that singular integrals of particular functions include binomial coefficients. In this paper, we prove combinatorial identities from the fact that two results of the particular function calculated as two ways using the residue theorem in the complex function theory are the same. These combinatorial identities are the generalization of a combinatorial identity that has been already obtained
Bargraphs are column convex polyominoes, where the lower edge lies on a horizontal axis. We consider the inner site-perimeter, which is the total number of cells inside the bargraph that have at least one edge in common with an outside cell and obtain the generating function that counts this statistic. From this we find the average inner perimeter and the asymptotic expression for this average as the semi-perimeter tends to infinity. We finally consider those bargraphs where the inner site-perimeter is exactly equal to the area of the bargraph.
Let
The
The main purposes of this paper are to introduce the
1970-2025 CP (Manitoba, Canada) unless otherwise stated.