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The aim of this work is to show how Riordan arrays are able to generate and close combinatorial identities, by means of the method of coefficients (generating functions). We also show how the same approach can be used to deal with other combinatorial problems, for instance asymptotic approximation and combinatorial inversion. Finally, we propose a method for generating new combinatorial sums by extending the concept of Riordan arrays to bi-infinite matrices. [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]