Complexity of cutting words on regular tilings

  • Authors:

  • Pascal Hubert;Laurent Vuillon

  • Affiliations:

  • Laboratoire d'Analyse, Topologie, Probabilités Case cour A, Faculté des Sciences de Saint Jérôme, Escadrille Normandie-Niemen, Marseille Cedex, France;Laboratoire de Mathématiques, Université de Savoie, le Bourget-du-Lac, France

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

We show that the complexity of a cutting word u in a regular tiling with a polyomino Q is equal to Pn(u) = (p + q - 1)n + 1 for all n ≥ 0, where Pn(u) counts the number of distinct factors of length n in the infinite word u and where the boundary of Q is constructed of 2p horizontal and 2q vertical unit segments.