We study the palindromic complexity of infinite words , the fixed points of the substitution over a binary alphabet, , , with , which are canonically associated with quadratic non-simple Parry numbers .
Keywords: palindromes, beta-expansions, infinite words
@article{ITA_2009__43_1_145_0, author = {Balkov\'a, L'ubom{\'\i}ra and Mas\'akov\'a, Zuzana}, title = {Palindromic complexity of infinite words associated with non-simple {Parry} numbers}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {145--163}, publisher = {EDP-Sciences}, volume = {43}, number = {1}, year = {2009}, doi = {10.1051/ita:2008005}, mrnumber = {2483448}, zbl = {1156.68043}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2008005/} }
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 - Informatique Théorique et Applications PY - 2009 SP - 145 EP - 163 VL - 43 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2008005/ DO - 10.1051/ita:2008005 LA - en ID - ITA_2009__43_1_145_0 ER -
%0 Journal Article %A Balková, L'ubomíra %A Masáková, Zuzana %T Palindromic complexity of infinite words associated with non-simple Parry numbers %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 145-163 %V 43 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2008005/ %R 10.1051/ita:2008005 %G en %F ITA_2009__43_1_145_0
Balková, L'ubomíra; Masáková, Zuzana. Palindromic complexity of infinite words associated with non-simple Parry numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 1, pp. 145-163. doi : 10.1051/ita:2008005. http://www.numdam.org/articles/10.1051/ita:2008005/
[1] Palindromic complexity of infinite words associated with simple Parry numbers. Annales de l'Institut Fourier 56 (2006) 2131-2160. | Numdam | MR | Zbl
, , and ,[2] Factor versus palindromic complexity of uniformly recurrent infinite words. Theor. Comp. Sci. 380 (2007) 266-275. | MR | Zbl
, and ,[3] L’. Balková, Complexity for infinite words associated with quadratic non-simple Parry numbers. J. Geom. Sym. Phys. 7 (2006) 1-11. | MR | Zbl
[4] 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. | Numdam | MR | Zbl
[5] L’. Balková, E. Pelantová and W. Steiner, Sequences with constant number of return words. Monatshefte fur Mathematik, to appear.
[6] Étude sur le -développement et applications. Mémoire de D.E.A., Université de la Méditerrannée Aix-Marseille (2002).
,[7] Beta-integers as natural counting systems for quasicrystals. J. Phys. A 31 (1998) 6449-6472. | MR | Zbl
, , and ,[8] Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators. Rev. Math. Phys. 15 (2003) 745-763. | MR | Zbl
and ,[9] Palindrome complexity bounds for primitive substitution sequences. Discrete Math. 222 (2000) 259-267. | MR | Zbl
and ,[10] Substitutions et -systèmes de numération. Theoret. Comput. Sci. 137 (1995) 219-236. | MR | Zbl
,[11] 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. | Numdam | MR | Zbl
, and ,[12] Infinite special branches in words associated with beta-expansions. Discrete Math. Theor. Comput. Sci. 9 (2007) 125-144. | MR | Zbl
, and ,[13] Singular continuous spectrum for palindromic Schrödinger operators. Commun. Math. Phys. 174 (1995) 149-159. | MR | Zbl
, and ,[14] Geometric models for quasicrystals I. Delone sets of finite type. Discrete Comput. Geom. 21 (1999) 161-191. | MR | Zbl
,[15] Quasicrystals, Diophantine approximation, and algebraic numbers, in Beyond Quasicrystals, edited by F. Axel, D. Gratias. EDP Sciences, Les Ulis; Springer, Berlin (1995) 6-13. | MR | Zbl
,[16] On the beta-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11 (1960) 401-416. | MR | Zbl
,[17] Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477-493. | MR | Zbl
,[18] On periodic expansions of Pisot numbers and Salem numbers. Bull. London Math. Soc. 12 (1980) 269-278. | MR | Zbl
,[19] Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53 (1984) 1951-1954.
, , and ,[20] Groups, tilings, and finite state automata. Geometry supercomputer project research report GCG1, University of Minnesota (1989).
,[21] Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers. RAIRO-Theor. Inf. Appl. 41 (2007) 123-135. | Numdam | MR | Zbl
,Cited by Sources: