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In this paper, by using Riordan arrays and a particular model of lattice paths, we are able to generalize in several ways an identity proposed by Lou Shapiro by giving both an algebraic and a combinatorial proof. The identities studied in this paper allow us to move from an arithmetic progression, and other C-finite sequences, to a geometric progression in terms of Riordan array transformations and vice versa, via the Riordan array inverse. [ABSTRACT FROM AUTHOR]

When planning a database, the problem of index selection is of particular interest. In this paper, we examine a transaction model which includes queries, updates, insertions, and deletions, and we define a function that calculates the transactions total cost when an index set is used. Our aim was to minimize the function cost in order to identify the optimal set. The algorithms proposed in other studies require an exponential time in the number of file attributes in order to solve the problem. We propose a heuristic algorithm based on some properties of the cost function and this algorithm produces an almost optimal set in polinomial time. In many cases, the cost function properties make it possible to prove that the solution obtained is the optimal one. [ABSTRACT FROM AUTHOR]

Abstract: Historically, there exist two versions of the Riordan array concept. The older one (better known as recursive matrix) consists of bi-infinite matrices ( implies ), deals with formal Laurent series and has been mainly used to study algebraic properties of such matrices. The more recent version consists of infinite, lower triangular arrays ( implies ), deals with formal power series and has been used to study combinatorial problems. Here we show that every Riordan array induces two characteristic combinatorial sums in three parameters . These parameters can be specialized and generate an indefinite number of other combinatorial identities which are valid in the bi-infinite realm of recursive matrices. [Copyright &y& Elsevier]