We first prove an extremal property of the infinite Fibonacci word : the family of the palindromic prefixes of is not only a circular code but “almost” a comma-free one (see Prop. 12 in Sect. 4). We also extend to a more general situation the notion of a necklace introduced for the study of trinucleotides codes on the genetic alphabet, and we present a hierarchy relating two important classes of codes, the comma-free codes and the circular ones.
Mots clés : theory of codes, comma-free codes, circular codes
@article{ITA_2008__42_4_717_0, author = {Pirillo, Giuseppe}, title = {A hierarchy for circular codes}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {717--728}, publisher = {EDP-Sciences}, volume = {42}, number = {4}, year = {2008}, doi = {10.1051/ita:2008002}, mrnumber = {2458703}, zbl = {1155.68069}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2008002/} }
TY - JOUR AU - Pirillo, Giuseppe TI - A hierarchy for circular codes JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 717 EP - 728 VL - 42 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2008002/ DO - 10.1051/ita:2008002 LA - en ID - ITA_2008__42_4_717_0 ER -
%0 Journal Article %A Pirillo, Giuseppe %T A hierarchy for circular codes %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 717-728 %V 42 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2008002/ %R 10.1051/ita:2008002 %G en %F ITA_2008__42_4_717_0
Pirillo, Giuseppe. A hierarchy for circular codes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 717-728. doi : 10.1051/ita:2008002. http://archive.numdam.org/articles/10.1051/ita:2008002/
[1] A complementary circular code in the protein coding genes. J. Theor. Biol. 182 (1996) 45-58.
and ,[2] A circular code in the protein coding genes of mitochondria. J. Theor. Biol. 189 (1997) 273-290.
and ,[3] Mots de Fibonacci. Séminaire d'informatique théorique. LITP, Paris (1980-81) 57-78.
,[4] Theory of codes. Academic Press (1985). | MR | Zbl
and ,[5] Sturmian words, in Algebraic Combinatorics on words, edited by M. Lothaire. Cambridge University Press (2002). | MR
and ,[6] Codes without commas. Proc. Natl. Acad. Sci. USA 43 (1957) 416-421. | MR
, and ,[7] A combinatorial property of the Fibonacci words. Inform. Process. Lett. 12 (1981) 193-195. | MR | Zbl
,[8] Sturmian words: structure, combinatorics, and their arithmetics. Theoret. Comput. Sci. 183 (1997) 45-82. | MR | Zbl
,[9] Palindromes in the Fibonacci word. Inform. Process Lett. 55 (1995) 217-221. | MR | Zbl
,[10] On some factorizations of infinite words by elements of codes. Inform. Process. Lett. 62 (1997) 289-294. | MR
and ,[11] On cube-free -words generated by binary morphism. Discrete Appl. Math. 5 (1983) 279-297. | MR | Zbl
,[12] The Art of Computer Programming. Addison-Wesley, Reading, Mass. (1968). | MR | Zbl
,[13] Fast pattern matching in strings. SIAM J. Comput. 6 (1977) 323-350. | MR | Zbl
, and ,[14] Combinatorics on words. Addison-Wesley (1983). | MR | Zbl
,[15] Varieties of comma-free codes. Comput. Math. Appl. (in press). | Zbl
, and ,[16] Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199-204. | EuDML | Numdam | MR | Zbl
and ,[17] Infinite words and biprefix codes. Inform. Process Lett. 50 293-295 (1994). | MR | Zbl
,[18] Fibonacci numbers and words. Discrete Math. 173 (1997) 197-207. | MR | Zbl
,[19] Some factorizations of the Fibonacci word. Algebra Colloquium 6 (1999) 361-368. | MR | Zbl
,[20] A characterization for a set of trinucleotides to be a circular code, In Determinism, Holism, and Complexity, edited by C. Pellegrini, P. Cerrai, P. Freguglia, V. Benci and G. Israel. Kluwer (2003).
,[21] Growth function of self-complementary circular codes. Biology Forum 98 (2005) 97-110.
and ,[22] Propriétés combinatoires des mots infinis engendrés par certains morphismes. PhD. thesis, L.I.T.P., Paris. (1985).
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