Substitution invariant cutting sequences

D. Crisp; W. Moran; A. Pollington; P. Shiue

Journal de théorie des nombres de Bordeaux (1993)

  • Volume: 5, Issue: 1, page 123-137
  • ISSN: 1246-7405

How to cite


Crisp, D., et al. "Substitution invariant cutting sequences." Journal de théorie des nombres de Bordeaux 5.1 (1993): 123-137. <>.

author = {Crisp, D., Moran, W., Pollington, A., Shiue, P.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {invariant substitution; cutting sequences; continued fraction expansions},
language = {eng},
number = {1},
pages = {123-137},
publisher = {Université Bordeaux I},
title = {Substitution invariant cutting sequences},
url = {},
volume = {5},
year = {1993},

AU - Crisp, D.
AU - Moran, W.
AU - Pollington, A.
AU - Shiue, P.
TI - Substitution invariant cutting sequences
JO - Journal de théorie des nombres de Bordeaux
PY - 1993
PB - Université Bordeaux I
VL - 5
IS - 1
SP - 123
EP - 137
LA - eng
KW - invariant substitution; cutting sequences; continued fraction expansions
UR -
ER -


  1. [1] T.C. Brown, A characterisation of the quadratic irrationals, Canad. Math. Bull.34 (1991), 36-41. Zbl0688.10007MR1108926
  2. [2] H. Cohn, Some direct limits of primitive homotopy words and of Markoff geodesics, Discontinuous groups and Riemann surfaces, Ann. of Math. Studies No. 79, Princeton Univ. Press, Princeton, N.J., (1974), 81-98. Zbl0294.20044MR369269
  3. [3] A.S. Fraenkel, Determination of [nθ] by its sequence of differences, Canad. Math. Bull.21 (1978), 441-446. Zbl0401.10018
  4. [4] Sh. Ito and S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx + y] - [(n - 1)x + y], Japan J. Math.16 (1990), 287-306. Zbl0721.11009MR1091163
  5. [5] C. Series, The geometry of Markoff numbers, Math. Intelligencer7 (1985), 20-29. Zbl0566.10024MR795536
  6. [6] K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull.19 (1976), 473-482. Zbl0359.10028MR444558

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  3. Jean-Pierre Borel, How to build billiard words using decimations
  4. Cyril Allauzen, Une caractérisation simple des nombres de Sturm
  5. Jeffrey Shallit, Automaticity IV : sequences, sets, and diversity
  6. Jacques Justin, Giuseppe Pirillo, Decimations and sturmian words
  7. J. Berstel, P. Séébold, A remark on morphic sturmian words
  8. S. de Bièvre, G. Forni, On the growth of averaged Weyl sums for rigid rotations
  9. Isabelle Fagnot, A little more about morphic Sturmian words
  10. Éric Laurier, Opérations sur les mots de Christoffel

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