On Coxeter recurrences

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An interesting family of recurrences of order n ≥ 2, which are globally (n+3)-periodic was introduced by Coxeter in 1971. We prove a surprising property of this family: 'all' the possible geometrical behaviours that linear real (n+3)-periodic recurrences can have are present inside the Coxeter recurrences. © 2012 Copyright Taylor and Francis Group, LLC.
Original languageEnglish
Pages (from-to)1457-1465
JournalJournal of Difference Equations and Applications
Publication statusPublished - 1 Sep 2012


  • Coxeter difference equations
  • globally periodic difference equations
  • linearization
  • recurrences


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