@article{3ed56204f5314bd5a248f254675e0f96,
title = "Riordan pseudo-involutions, continued fractions and somos-4 sequences",
abstract = "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.",
keywords = "A-sequence, B-sequence, Elliptic curve, Hankel transform, Recurrence, Riordan array, Riordan pseudo-involution, Somos sequence",
author = "Paul Barry",
note = "Funding Information: Many of the techniques used in this paper are based on investigations into elliptic curves and the fascinating Somos sequences, themselves originating in the elliptic divisibility sequences [18], and further elaborated by Michael Somos, whose creative mathematics and many relevant contributions to the Online Encyclopedia of Integer Sequences [15, 16] have been inspirational. I would like to thank the anonymous reviewer whose constructive comments have helped to clarify many points of this exposition. This paper was completed while the author was a guest of the Applied Algebra and Optimization Research Center (AORC) of Sungkyunkwan University, Suwon, South Korea, and the author wishes to express his appreciation for their hospitality. Publisher Copyright: {\textcopyright} 2019, University of Waterloo. All rights reserved.",
year = "2019",
language = "English",
volume = "22",
journal = "Journal of Integer Sequences",
issn = "1530-7638",
publisher = "University of Waterloo",
number = "6",
}