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- Renzo Sprugnoli
- Discrete Mathematics
- 1994

- Renzo Sprugnoli
- Discrete Mathematics
- 1995

We generalize the well-known identities of Abel and Gould in the context of Riordan arrays. This allows us to prove analogous formulas for Stirling numbers of both kinds and also for other quantities.

- Renzo Sprugnoli
- Commun. ACM
- 1977

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)

- D Merlini, D G Rogers, R Sprugnoli, M C Verri, Bs, Cs
- 2005

We use some combinatorial methods to study underdiagonal paths on the Z lat tice made up of unrestricted steps i e ordered pairs of non negative integers We introduce an algorithm which automatically produces some counting generating func tions for a large class of these paths We also give an example of how we use these functions to obtain some speci c… (More)

- Cristiano Corsani, Donatella Merlini, Renzo Sprugnoli
- Discrete Mathematics
- 1998

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 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)

- Donatella Merlini, Renzo Sprugnoli, M. Cecilia Verri
- The American Mathematical Monthly
- 2007

can be found in closed form by means of certain transformations on generating functions and the extraction of coefficients (see the end of section 3) suggested by Ira Gessel, and they comment: “He [Gessel] attributes this elegant technique, the ‘method of coefficients,’ to G. P. Egorychev.” Actually, in his book Integral Representation and Computation of… (More)

The concept of generating trees has been introduced in the literature by Chung, Graham, Hoggat and Kleiman in [4] to examine Baxter permutations. This technique has been successfully applied by West [17, 18] to other classes of permutations and more recently to some other combinatorial classes such as plane trees and lattice paths (see Barcucci et al. [2]).… (More)

- Elena Barcucci, Renzo Pinzani, Renzo Sprugnoli
- IEEE Trans. Software Eng.
- 1990

The aim of the present paper is to show how the Lagrange Inversion Formula (LIF) can be applied in a straight-forward 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)