# Palindromic complexity of infinite words associated with non-simple Parry numbers

L'ubomíra Balková; Zuzana Masáková

RAIRO - Theoretical Informatics and Applications (2008)

- Volume: 43, Issue: 1, page 145-163
- ISSN: 0988-3754

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topBalková, L'ubomíra, and Masáková, Zuzana. "Palindromic complexity of infinite words associated with non-simple Parry numbers." RAIRO - Theoretical Informatics and Applications 43.1 (2008): 145-163. <http://eudml.org/doc/92903>.

@article{Balková2008,

abstract = {
We study the palindromic complexity of infinite words uβ,
the fixed points of the substitution over a binary alphabet,
φ(0) = 0a1, φ(1) = 0b1, with a - 1 ≥ b ≥ 1,
which are canonically associated with quadratic non-simple Parry
numbers β.
},

author = {Balková, L'ubomíra, Masáková, Zuzana},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Palindromes; beta-expansions; infinite words.; palindromes; infinite words},

language = {eng},

month = {3},

number = {1},

pages = {145-163},

publisher = {EDP Sciences},

title = {Palindromic complexity of infinite words associated with non-simple Parry numbers},

url = {http://eudml.org/doc/92903},

volume = {43},

year = {2008},

}

TY - JOUR

AU - Balková, L'ubomíra

AU - Masáková, Zuzana

TI - Palindromic complexity of infinite words associated with non-simple Parry numbers

JO - RAIRO - Theoretical Informatics and Applications

DA - 2008/3//

PB - EDP Sciences

VL - 43

IS - 1

SP - 145

EP - 163

AB -
We study the palindromic complexity of infinite words uβ,
the fixed points of the substitution over a binary alphabet,
φ(0) = 0a1, φ(1) = 0b1, with a - 1 ≥ b ≥ 1,
which are canonically associated with quadratic non-simple Parry
numbers β.

LA - eng

KW - Palindromes; beta-expansions; infinite words.; palindromes; infinite words

UR - http://eudml.org/doc/92903

ER -

## References

top- P. Ambrož, Ch. Frougny, Z. Masáková and E. Pelantová, Palindromic complexity of infinite words associated with simple Parry numbers. Annales de l'Institut Fourier56 (2006) 2131–2160.
- P. Baláži, Z. Masáková and E. Pelantová, Factor versus palindromic complexity of uniformly recurrent infinite words. Theor. Comp. Sci.380 (2007) 266–275.
- L'. Balková, Complexity for infinite words associated with quadratic non-simple Parry numbers. J. Geom. Sym. Phys.7 (2006) 1–11.
- L'. Balková, E. Pelantová and O. Turek, Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers. RAIRO-Theor. Inf. Appl.41 (2007) 307–328.
- L'. Balková, E. Pelantová and W. Steiner, Sequences with constant number of return words. Monatshefte fur Mathematik, to appear.
- J. Bernat, Étude sur le β-développement et applications. Mémoire de D.E.A., Université de la Méditerrannée Aix-Marseille (2002).
- Č. Burdík, Ch. Frougny, J.P. Gazeau and R. Krejcar, Beta-integers as natural counting systems for quasicrystals. J. Phys. A31 (1998) 6449–6472.
- D. Damanik and L.Q. Zamboni, Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Rev. Math. Phys.15 (2003) 745–763.
- D. Damanik and D. Zare, Palindrome complexity bounds for primitive substitution sequences. Discrete Math.222 (2000) 259–267.
- S. Fabre, Substitutions et β-systèmes de numération. Theoret. Comput. Sci.137 (1995) 219–236.
- Ch. Frougny, Z. Masáková and E. Pelantová, Complexity of infinite words associated with beta-expansions. RAIRO-Theor. Inf. Appl.38 (2004), 163–185; Corrigendum. RAIRO-Theor. Inf. Appl.38 (2004) 269–271.
- Ch. Frougny, Z. Masáková and E. Pelantová, Infinite special branches in words associated with beta-expansions. Discrete Math. Theor. Comput. Sci.9 (2007) 125–144.
- A. Hof, O. Knill and B. Simon, Singular continuous spectrum for palindromic Schrödinger operators. Commun. Math. Phys.174 (1995) 149–159.
- J. Lagarias, Geometric models for quasicrystals I. Delone sets of finite type. Discrete Comput. Geom.21 (1999) 161–191.
- Y. Meyer, Quasicrystals, Diophantine approximation, and algebraic numbers, in Beyond Quasicrystals, edited by F. Axel, D. Gratias. EDP Sciences, Les Ulis; Springer, Berlin (1995) 6–13.
- W. Parry, On the beta-expansions of real numbers. Acta Math. Acad. Sci. Hungar.11 (1960) 401–416.
- A. Rényi, Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar.8 (1957) 477–493.
- K. Schmidt, On periodic expansions of Pisot numbers and Salem numbers. Bull. London Math. Soc.12 (1980) 269–278.
- D. Shechtman, I. Blech, D. Gratias and J. Cahn, Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett.53 (1984) 1951–1954.
- W.P. Thurston, Groups, tilings, and finite state automata. Geometry supercomputer project research report GCG1, University of Minnesota (1989).
- O. Turek, Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers. RAIRO-Theor. Inf. Appl.41 (2007) 123–135.

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