| Title:
|
Regular maps in generalized number systems (English) |
| Author:
|
Allouche, Jean-Paul |
| Author:
|
Scheicher, Klaus |
| Author:
|
Tichy, Robert Franz |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
41-58 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A63 |
| MSC:
|
11B85 |
| MSC:
|
11R11 |
| idZBL:
|
Zbl 0957.11014 |
| idMR:
|
MR1764344 |
| . |
| Date available:
|
2009-09-25T11:42:11Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133301 |
| . |
| Reference:
|
[1] ALLOUCHE J.-P.: q-regular sequences and other generalizations of q-automatic sequences.In: Lecture Notes in Comput. Sci. 583, Springer, Nеw York, 1992, pp. 15-23. MR 1253343 |
| Reference:
|
[2] ALLOUCHE J.-P.: Finite automata and arithmetic.In: Seminairе Lotharingiеn dе Combinatoire BЗ0c, 1993, pp. 1-23. Zbl 0903.11009, MR 1312624 |
| Reference:
|
[3] ALLOUCHE J.-P.-CATELAND E.-GILBERT W. J.-PEITGEN H.-O.- SHALLIT J.-SKORDEV G.: Automatic maps in exotic numeration systems.Theory Comput. Syst. (Formerly: Math. Systems Theory) 30 (1997), 285-331. MR 1432196 |
| Reference:
|
[4] ALLOUCHE J.-P.-MORTON P.-SHALLIT J.: Pattern spectra, substring enumeration, and automatic sequences.Theoret. Comput. Sci. 94 (1.992), 161-174. Zbl 0753.11012, MR 1157853 |
| Reference:
|
[5] ALLOUCHE J.-P.-SHALLIT J.: The ring of k-regular sequences.Theoret. Comput. Sci. 98 (1992), 163-187. Zbl 0774.68072, MR 1166363 |
| Reference:
|
[6] CHRISTOL G.: Ensembles presque-periodiques k-reconnaissables.Theoret. Comput. Sci. 9 (1979), 141-145. Zbl 0402.68044, MR 0535129 |
| Reference:
|
[7] CHRISTOL G.-KAMAE T.-MENDES FRANCE M.-RAUZY G.: Suites algebriques, automates et substitutions.Bull. Soc. Math. France 108 (1980), 401-419. MR 0614317 |
| Reference:
|
[8] COBHAM A.: On the base-dependence of sets of numbers recognizable by finite automata.Math. Systems Theory 3 (1969), 186-192. Zbl 0179.02501, MR 0250789 |
| Reference:
|
[9] COBHAM A.: Uniform tag sequences.Math. Systems Theory 6 (1972), 164-192. Zbl 0253.02029, MR 0457011 |
| Reference:
|
[10] DEKKING F. M.-MENDES FRANCE M.-VAN DER POORTEN A. J.: Folds!.Math. Intelligencer 4 (1982), 130-138, 173-181, 190-195. MR 0684028 |
| Reference:
|
[11] FRAENKEL A. S.: Systems of numeration.Amer. Math. Monthly 92 (1985), 105-114. Zbl 0568.10005, MR 0777556 |
| Reference:
|
[12] FROUGNY C.: Confluent linear numeration systems.Theoret. Comput. Sci. 106 (1992), 183-219. Zbl 0787.68057, MR 1192767 |
| Reference:
|
[13] FROUGNY C.-SOLOMYAK B.: On representation of integers in linear numeration systems.In: Ergodic Theory of Zd actions. Proceedings of the Warwick Symposium, Warwick, UK, 1993-94 (M. Pollicott et al., eds.), London Math. Soc. Lecture Note Ser. 228, Cambridge University Press, Cambridge, 1996, pp. 345-368. MR 1411227 |
| Reference:
|
[14] GRABNER P. G.-KIRSCHENHOFER P.-PRODINGER H.: The sum of digits function for complex bases.J. London Math. Soc. 57 (1998), 20-40. Zbl 0959.11045, MR 1624777 |
| Reference:
|
[15] KÁTAI I.-KOVÁCS B.: Kanonische Zahlensysteme in der Theorie der quadratischen algebraischen Zahlen.Acta Sci. Math. (Szeged) 42 (1980), 99-107. Zbl 0386.10007, MR 0576942 |
| Reference:
|
[16] KÁTAI I.-KOVÁCS B.: Canonical number systems in imaginary quadratic fields.Acta Math. Acad. Sci. Hungar. 37 (1981), 159-164. Zbl 0477.10012, MR 0616887 |
| Reference:
|
[17] KÁTAI I.-SZABO J.: Canonical number systems for complex integers.Acta Sci. Math. (Szeged) 37 (1975), 255-260. Zbl 0309.12001, MR 0389759 |
| Reference:
|
[18] KIMBERLING C.: Numeration systems and fractal sequences.Acta Arith. 73 (1995), 103-117. Zbl 0834.11010, MR 1358191 |
| Reference:
|
[19] KNUTH D. E.: The Art of Computer Programming.Vol. 2. Seminumerical Algorithms (2nd ed.), Addison Wesley, Reading, 1981. Zbl 0477.65002, MR 0633878 |
| Reference:
|
[20] KOVÁCS B.: CNS rings.In: Topics in Classical Number Theory, Vol. II (G. Halasz, ed.), Colloq. Math. Soc. Janos Bolyai 34, North-Holland, Amsterdam, 1984, pp. 961-971. Zbl 0558.10006, MR 0781170 |
| Reference:
|
[21] KOVÁCS B.-PETHO A.: Number systems in integral domains, especially in orders of algebraic number fields.Acta Sci. Math. (Szeged) 55 (1991), 287-299. Zbl 0760.11002, MR 1152592 |
| Reference:
|
[22] MORTON P.-MOURANT W.: Paper folding, digit patterns and groups of arithmetic fractals.Proc. London Math. Soc. 59 (1989), 253-293. Zbl 0694.10009, MR 1004431 |
| Reference:
|
[23] SALON O.: Suites automatiques á multi-indices et algebricité.C. R. Acad. Sci. Paris Ser. I Math. 305 (1987), 501-504. Zbl 0628.10007, MR 0916320 |
| Reference:
|
[24] SALON O.: Proprietes arithmetiques des automates multidimensionnels.Thése, University Bordeaux I, Bordeaux, 1989. |
| Reference:
|
[25] SCHEICHER K.: Kanonische Ziffernsysteme und Automaten.In: Grazer Math. Ber. 333, Karl-Franzens-Univ. Graz, Graz, 1997, pp. 1-17. MR 1640469 |
| Reference:
|
[26] SCHEICHER K.: Zifferndarstellungen, lineare Rekursionen und Automaten.PhD Thesis, TU Graz, Graz, 1997. |
| Reference:
|
[27] SHALLIT J.: A generalization of automatic sequences.Theoret. Comput. Sci. 61 (1988), 1-16. Zbl 0662.68052, MR 0974766 |
| Reference:
|
[28] THUSWALDNER J.: Elementary properties of canonical number systems in quadratic fields.In: Applications of Fibonacci Numbers, Vol. 7 (Graz 1996), Kluwer Acad. Publ., Dordrecht, 1998, pp. 405-414. MR 1638467 |
| . |
