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

Paul Barry

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Article number19.6.1
JournalJournal of Integer Sequences
Volume22
Issue number6
Publication statusPublished - 2019

Keywords

  • A-sequence
  • B-sequence
  • Elliptic curve
  • Hankel transform
  • Recurrence
  • Riordan array
  • Riordan pseudo-involution
  • Somos sequence

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