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Prodotti recenti

On One-Parameter Catalan Arrays

We present a parametric family of Riordan arrays, which are obtained by multiplying any Riordan array with a generalized Pascal array. In particular we focus on some interesting properties of one-parameter Catalan triangles. -We obtain several combinatorial identities that involve two specia...

A symbolic treatment of Riordan arrays

We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel's identity for polynomials. In particular,...

A symbolic treatment of Abel polynomials

We study the umbral polynomials A(k)n(x, α) = x(x-k·α) n-1, by means of which a wide range of formal power series identities, including Lagrange inversion formula, can be usefully manipulated. We apply this syntax within cumulant theory, and show how moments and its formal cum...

Outcomes of the Abel Identity

We discuss some outcomes of an umbral generalization of the Abel identity. First we prove that a concise proof of the Lagrange inversion formula can be deduced from it. Second, we show that the whole class of Sheffer sequences, if manipulated to an umbral level, coincides...

Combinatorics of a generalized Narayana identity

The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums of the ordinary Narayana numbers. In this paper we generalize the Narayana identity to a family of Riordan arrays including the array of ballot numbers, the classical Catalan triangle...