Riordan Pseudo-Involutions, Continued Fractions and Somos-4 Sequences
School of Science
Waterford Institute of Technology
We define a three-parameter family of Bell pseudo-involutions in the
Riordan group. The defining sequences have generating functions
that are expressible as continued fractions. We indicate that the
Hankel transforms of the defining sequences, and of the A sequences
of the corresponding Riordan arrays, can be associated with a Somos-4
sequence. We give examples where these sequences can be associated
with elliptic curves, and we exhibit instances where elliptic curves
can give rise to associated Riordan pseudo-involutions. In the case of
a particular one-parameter family of elliptic curves, we show how we can
associate a unique Bell pseudo-involution with each such curve.
Full version: pdf,
(Concerned with sequences
Received July 16 2018; revised versions received July 18 2018; June 27 2019.
Published in Journal of Integer Sequences,
August 24 2019.
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