Related papers: Composition of ordinary generating functions
A superdiagonal composition is one in which the $i$-th part or summand is of size greater than or equal to $i$. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In…
Lexicographic composition is a natural way to build an aggregate choice function from component choice functions. As the name suggests, the components are ordered and choose sequentially. The sets that subsequent components select from are…
Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated Lie algebra are proposed. It is shown that in the second…
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world…
In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions…
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
The basis of this work is a simple, extended corollary of Wilson's theorem. This corollary generates many more quotients than those already generated by Wilson's theorem, and it was of interest to derive how they relate to each other and…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…
Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…
Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As special cases of the multilinear generating…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
We study the existence of a common hypercyclic vector for different families of composition operators.
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is that this family satisfies a rational recursion and are…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.