Associativity of recurrence multiplication

P. J. Grabner*, A. Pethő, R. F. Tichy, G. J. Woeginger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An extension of Knuth's Fibonacci multiplication to recurrences G k+d = a1G k+d-1 + ⋯ + a d G k with a 1 ≥ a 2 ≥ ⋯ ≥ a d \2>0 and "canonical" initial values G k = a 1 G k-1 + a 2 G k-2 + ⋯ + a k G 0 + 1, 0 ≤ k < d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large.

Original languageEnglish
Pages (from-to)85-90
Number of pages6
JournalApplied Mathematics Letters
Issue number4
Publication statusPublished - Jul 1994


  • Digit expansions
  • Linear recurrences
  • Pisot numbers.
  • β-shift

ASJC Scopus subject areas

  • Applied Mathematics


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