7 citations · 22 across the 8 of their papers we have counts for
9 papers
A Symbolic Treatment of Riordan Arrays
José Agapito, Ângela Mestre, Pasquale Petrullo +1
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 immed…
On One-Parameter Catalan Arrays
José Agapito, Ângela Mestre, Pasquale Petrullo +1
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 pr…
Hall-Littlewood symmetric functions via Yamanouchi toppling game
Robert Cori, Pasquale Petrullo, Domenico Senato
We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. The game arises from the well-known chip-firing game when the usual relation of equiv…
Orthogonal polynomials through the invariant theory of binary forms
Pasquale Petrullo, Domenico Senato, Rosaria Simone
We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward…
Outcomes of the Abel Identity
Pasquale Petrullo
Through symbolic methods, we state explicit formulae for Tchebychev, Gegenbauer, Meixner, Mittlag-Leffler, and Pidduck polynomials. This is done by underlining the crucial role pla…
Riordan arrays and applications via the classical umbral calculus
José Agapito, Ângela Mestre, Pasquale Petrullo +1
We use the classical umbral calculus to describe Riordan arrays. Here, a Riordan array is generated by a pair of umbrae, and this provides efficient proofs of several basic results…