This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials.

We study basis partitions, introduced by Hansraj Gupta in 1978. For this family of partitions, we give a recurrence, a generating function, identities relating basis partitions to more familiar families of partitions, and a new characterization of basis partitions.

The idea of graph compositions generalizes both ordinary compositions of positive integers and partitions of finite sets. In this paper we develop formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs.

The authors apply a certain novel technique based on the combined use of operational methods and of some special multivariable and multiindex polynomials to derive several families of generating functions involving the products of Bessel and related functions. The possibility of extending this technique to the derivation of generating functions of hybrid nature (involving, for example, the prod...

We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these fami...

Iterated finite state sequential transducers are considered as language generating devices. The hierarchy induced by the size of the state alphabet is proved to collapse to the fourth level. The corresponding language families are related to the families of languages generated by Lindenmayer systems and Chomsky grammars. Finally, some results on deterministic and extended iterated finite state ...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

Let G be a finite group. By Riemann’s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discuss several applications, including the cl...

Using the language of exponential Riordan arrays, we study three distinct families of orthogonal polynomials defined by trigonometric functions. We study the moment sequences of theses families, finding continued fraction expressions for their generating functions, and calculate the Hankel transforms of these moment sequences. Results related to the Euler or zigzag numbers, as well as the gener...