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

Citations in EuDML Documents

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  2. J.-P. Borel, F. Laubie, Quelques mots sur la droite projective réelle
  3. Cyril Allauzen, Une caractérisation simple des nombres de Sturm
  4. Jean-Pierre Borel, How to build billiard words using decimations
  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. Éric Laurier, Opérations sur les mots de Christoffel
  10. Bruno Parvaix, Propriétés d'invariance des mots sturmiens

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