12 citations · 86 across the 51 of their papers we have counts for
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Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method…
Colored compositions, Invert operator and elegant compositions with the "black tie"
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an importan…
Construction and Composition of Rooted Trees via Descent Functions
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study…
Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials
Stefano Barbero, Umberto Cerruti, Nadir Murru +1
In this paper we highlight the connection between Ramanujan cubic polynomials (RCPs) and a class of polynomials, the Shanks cubic polynomials (SCPs), which generate cyclic cubic fi…