Relation between powers of factors and the recurrence function characterizing Sturmian words

  • Authors:

  • Z. Masáková;E. Pelantová

  • Affiliations:

  • Doppler Institute & Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic;Doppler Institute & Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

In this paper we use the relation of the index of an infinite aperiodic word and its recurrence function to give another characterization of Sturmian words. As a by-product, we give a new proof of the theorem describing the index of a Sturmian word in terms of the continued fraction expansion of its slope. This theorem was independently proved in [A. Carpi, A. de Luca, Special factors, periodicity, and an application to Sturmian words, Acta Inform. 36 (2000) 983-1006] and [D. Damanik, D. Lenz, The index of Sturmian sequences, European J. Combin. 23 (2002) 23-29].