Conversion between two multiplicatively dependent linear numeration systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2286, Issue , 2002, Pages 64-75

  Frougny, Christiane ^a,b  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b UNIVERSITÉ PARIS 8   (France)

Author keywords

[No Author keywords available]

Indexed keywords

POLYNOMIALS;

CHARACTERISTIC POLYNOMIALS; MINIMAL POLYNOMIALS; NUMERATION SYSTEMS; PISOT NUMBERS;

NUMBER THEORY;

EID: 23044532690     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45995-2_11     Document Type: Conference Paper

References (18)

1. M.-J. Bertin, A.Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse, J.-P. Schreiber, Pisot and Salem numbers, Birkhȁauser, 1992.
2. A. Bertrand, Développements en base de Pisot et répartition modulo 1. C.R. Acad. Sc., Paris 285 (1977), 419–421.
3. A. Bertrand-Mathis, Comment écrire les nombres entiers dans une base qui n’est pas entière. Acta Math. Acad. Sci. Hungar. 54 (1989), 237–241.
4. A. Bès, An extension of the Cobham-Semënov Theorem. Journal of Symbolic Logic 65 (2000), 201–211.
5. J.R. Bȕuchi, Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. 6 (1960), 66–92.
6. V. Bruyère and G. Hansel, Bertrand numeration systems and recognizability. Theoret. Comp. Sci. 181 (1997), 17–43.
7. A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata. Math. Systems Theory 3 (1969), 186–192.
8. F. Durand, A generalization of Cobham’s Theorem. Theory of Computing Systems 31 (1998), 169–185.
9. S. Eilenberg, Automata, Languages and Machines, vol. A, Academic Press, 1974.
10. S. Fabre, Une généralisation du théorème de Cobham. Acta Arithm. 67 (1994), 197–208.
11. A.S. Fraenkel, Systems of numeration. Amer. Math. Monthly 92(2) (1985), 105–114.
12. Ch. Frougny, Representation of numbers and finite automata. Math. Systems Theory 25 (1992), 37–60.
13. Ch. Frougny, Numeration Systems, Chapter 7 in M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, to appear, available at http://www-igm.univ-mlv.fr/∼berstel/Lothaire/index.html
14. Ch. Frougny and J. Sakarovitch, Automatic conversion from Fibonacci representation to representation in base ϕ, and a generalization. Internat. J. Algebra Comput. 9 (1999), 351–384.
15. Ch. Frougny and B. Solomyak, On Representation of Integers in Linear Numeration Systems, In Ergodic theory of Zd-Actions, edited by M. Pollicott and K. Schmidt, London Mathematical Society Lecture Note Series 228 (1996), Cambridge University Press, 345–368.
16. Ch. Frougny and B. Solomyak, On the context-freeness of the θ-expansions of the integers. Internat. J. Algebra Comput. 9 (1999), 347–350.
17. A. Rényi, Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957), 477–493.
18. A. L. Semënov, The Presburger nature of predicates that are regular in two number systems. Siberian Math. J. 18 (1977), 289–299.