Renzo Sprugnoli

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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)
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)
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 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)