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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 nnk p k (r))t n ]d(t): Since we already know the asymptotic value of t n ]d(t), we o n l y h a ve to compute p k (r) f o r every… (More)
The aim of the present paper is to show how the Lagrange Inversion Formula (LIF) can be applied in a straightforward way i) to find the generating function of many combinatorial sequences, ii) to extract the coefficients of a formal power series, iii) to compute combinatorial sums, and iv) to perform the inversion of combinatorial identities. Particular… (More)
We give several new characterizations of Riordan Arrays, the most important of which is: if fd n;k g n;k2N is a lower triangular array whose generic element d n;k linearly depends on the elements in a well-deened though large area of the array, then fd n;k g n;k2N is Riordan. We also provide some applications of these characterizations to the lattice path… (More)
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.
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)
This paper presents a data mining methodology to analyze the careers of University graduated students. We present different approaches based on clustering and sequential patterns techniques in order to identify strategies for improving the performance of students and the scheduling of exams. We introduce an ideal career as the career of an ideal student… (More)