Riordan pseudo-involutions, continued fractions and somos-4 sequences

Barry, Paul (2019) Riordan pseudo-involutions, continued fractions and somos-4 sequences. Journal of Integer Sequences, 22 (6). ISSN 1530-7638

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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.

Item Type: Article
Additional Information: 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: © 2019, University of Waterloo. All rights reserved.
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2607
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Depositing User: Admin SSL
Date Deposited: 19 Oct 2022 23:07
Last Modified: 04 Jul 2023 03:20

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