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The inversion of combinatorial sums is a fundamental problem in algebraic combinatorics. Some combinatorial sums, such as a n = P k d n;k b k , can not be inverted in terms of the orthogonality relation because the innnite, lower triangular array P = fd n;k g's diagonal elements are equal to zero (except d 0;0). Despite this, we can nd a left-inverse P such… (More)

We study many properties of Cauchy numbers in terms of generating functions and Riordan arrays and find several new identities relating these numbers with Stir-ling, Bernoulli and harmonic numbers. We also reconsider the Laplace summation formula showing some applications involving the Cauchy numbers.

A refinement of hashing which allows retrieval of an item in a static table with a single probe is considered. Given a set I of identifiers, two methods are presented for building, in a mechanical way, perfect hashing functions, i.e. functions transforming the elements of I into unique addresses. The first method, the “quotient reduction”… (More)

We wish to thank the anonymous referee whose comments helped us in improving the contents and readibility of our paper. 16 dominating singularity t = r of d(t). By a well-known result (see Bender 1], Theorem 2), it follows that d n;k p k (r))t n ]d(t): Since we already know the asymptotic value of t n ]d(t), we only have to compute p k (r) for every k 2 N.… (More)