Combinatorics of periods in strings

Journal of Combinatorial Theory. Series A

Volumn 104, Issue 1, 2003, Pages 95-113

  Rivals, Eric ^a   Rahmann, Sven ^b  

^a LIRMM   (France)

^b MAX PLANCK INSTITUTE FOR MOLECULAR GENETICS   (Germany)

Author keywords

Autocorrelation; Lattice; Periods; Strings

Indexed keywords

EID: 0345446602     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-3165(03)00123-7     Document Type: Article

References (22)

1. P. Billingsley, Probability and Measure, 3rd Edition, Wiley, New York, 1995.
2. S. Burkhardt, A. Crauser, P. Ferragina, H.-P. Lenhof, E. Rivals, M. Vingron, q-Gram based database searching using a suffix array (QUASAR), in: Third Annual International Conference on Computational Molecular Biology, Lyon, France, 11-14 April 1999, ACM Press, New York, pp. 77-83.
3. C. Choffrut, J. Karhumäki, Combinatorics of words, in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, Vol. 1, Springer, Berlin, 1997, pp. 329-438.
4. M. Crochemore, W. Rytter, Text Algorithms, Oxford University Press, Oxford, 1994.
5. N.G. DeBruijn, On Mahler's partition problem, Proc. Akad. Wet. Amsterdam 51 (1948) 659-669.
6. J.A. Fill, An interruptible algorithm for perfect sampling via markov chains, Ann. Appl. Probability 8 (1) (1998) 131-162.
7. N.J. Fine, H.S. Wilf, Uniqueness theorems for periodic functions, Proc. Amer. Math. Soc. 16 (1965) 109-114.
8. C.-E. Fröberg, Accurate estimation of the number of binary partitions, BIT 17 (1977) 386-391.
9. L.J. Guibas, A.M. Odlyzko, Periods in strings, J. Combin. Theory Ser. A 30 (1981) 19-42.
10. D. Gusfield, Algorithms on Strings, Trees and Sequences, Cambridge University Press, Cambridge, 1997.
11. P. Jokinen, J. Tarhio, E. Ukkonen, A comparison of approximate string matching algorithms, Software Practice and Experience 26 (12) (1996) 1439-1458.
12. D.E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, Vol. 2, 3rd Edition, Addison-Wesley, Reading, MA, 1998.
13. M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, Cambridge, 1999 URL: http://www-igm.univ-mlv.fr/~berstel/Lothaire/index.html.
14. G. Marsaglia, A. Zaman, Monkey tests for random number generators, Comput. Math. Appl. 26 (9) (1993) 1-10.
15. O. Owolabi, D.R. McGregor, Fast approximate string matching, Software Practice Exp. 18 (4) (1988) 387-393.
16. O.E. Percus, P.A. Whitlock, Theory and application of marsaglia's monkey test for pseudorandom number generators, ACM Trans. Modeling Comput. Simulation 5 (2) (1995) 87-100.
17. P. Pevzner, Computational Molecular Biology, MIT Press, Cambridge, MA, 2000.
18. S. Rahmann, E. Rivals, Exact and Efficient Computation of the expected number of missing and common words in random texts, in: R. Giancarlo, D. Sankoff (Eds.), Proceedings of the 11th Symposium on Combinatorial Pattern Matching, Lecture Notes in Computer Science, Vol. 1848, Springer, Berlin, 2000, pp. 375-387.
19. S. Rahmann, E. Rivals, The number of missing words in random texts, Combin. Probab. Comput. 12 (2003) 73-87.
20. E. Rivals, S. Rahmann, Combinatorics of periods in strings, in: F. Orejas, P. Spirakis, J. van Leuween (Eds.), Proceedings of the 28th ICALP, Lecture Notes in Computer Science, Vol. 2076, Springer, Berlin, 2001, pp. 615-626.
21. R. Sedgewick, P. Flajolet, Analysis of Algorithms, Addison-Wesley, Reading, MA, 1996.
22. E. Ukkonen, Approximate string-matching with q-grams and maximal matches, Theoret. Comput. Sci. 92 (1) (1992) 191-211.