On Convolved Generalized Fibonacci and Lucas Polynomials

We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices

Information systems offshore outsourcing: a descriptive analysis

Purpose - The present paper has as its aim to deepen in the study of Information Systems Offshore Outsourcing, proposing three essential steps to make this decision: weighing up the advantages and risks of Offshore Outsourcing; analysing the taxonomy of this phenomenon; and determining its current geography. Design/Methodology/Approach - With that objective in mind, it was decided to base the research work on the literature about this topic and the review of reports and statistics coming from different sources (consultants, the press, public institutions, etc.). Findings - Offshore Outsourcing has grown vertiginously in recent years. Its advantages exceed even those of onshore outsourcing, though it also involves greater risks derived from the (cultural and physical) distance existing between customer and provider. Various types of services and customer-provider relationships hide under the umbrella of Offshore Outsourcing; i.e. it is not a homogeneous phenomenon. The main Offshore Outsourcing customers can be found in the USA and Europe, mainly in the UK but also in other countries such as Germany and France. As for provider firms, most of them are located in Asia −outstandingly in India but also in China and Russia. At present, there are important providers scattered in other continents as well. Originality/Value - The conclusions suggest that the range of potential Offshore Outsourcing destinations must be widened and that the search for a provider cannot be based exclusively on cost savings; other considerations such as quality, security and proximity of the provider must also be taken into consideration. That is precisely the reason why the study of new countries like Spain as Offshore Outsourcing destinations is proposed

Restricted rr-Stirling Numbers and their Combinatorial Applications

We study set partitions with $r$ distinguished elements and block sizes found in an arbitrary index set $S$. The enumeration of these $(S,r)$-partitions leads to the introduction of $(S,r)$-Stirling numbers, an extremely wide-ranging generalization of the classical Stirling numbers and the $r$-Stirling numbers. We also introduce the associated $(S,r)$-Bell and $(S,r)$-factorial numbers. We study fundamental aspects of these numbers, including recurrence relations and determinantal expressions. For $S$ with some extra structure, we show that the inverse of the $(S,r)$-Stirling matrix encodes the M\"obius functions of two families of posets. Through several examples, we demonstrate that for some $S$ the matrices and their inverses involve the enumeration sequences of several combinatorial objects. Further, we highlight how the $(S,r)$-Stirling numbers naturally arise in the enumeration of cliques and acyclic orientations of special graphs, underlining their ubiquity and importance. Finally, we introduce related $(S,r)$ generalizations of the poly-Bernoulli and poly-Cauchy numbers, uniting many past works on generalized combinatorial sequences