The exact number of squares in Fibonacci words

Theoretical Computer Science

Volumn 218, Issue 1, 1999, Pages 95-106

  Fraenkel, Aviezri S ^a   Simpson, Jamie ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b CURTIN UNIVERSITY   (Australia)

Author keywords

Fibonacci words; Repetitions; Squares

Indexed keywords

EID: 0006937138     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00252-7     Document Type: Article

References (11)

1. M. Crochemore, An optimal algorithm for computing the repetitions in a word, Inform. Process. Lett. 12 (1981) 244-250.
2. M. Crochemore, W. Rytter, Text Algorithms, Oxford University Press, New York, 1994.
3. M. Crochemore, W. Rytter, Squares, cubes, and time-space efficient string searching, Algorithmica 13 (1995) 405-425.
4. A. de Luca, S. Varricchio, A combinatorial theorem on p-power-free words and an application to semigroups, RAIRO Inform. Theor. Appl. 24 (1990) 205-228.
5. A.S. Fraenkel, M. Mushkin, U. Tassa, Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978) 441-446.
6. A.S. Fraenkel, R.J. Simpson, How many squares can a string contain? J. Combinat. Theory (Ser. A) 82 (1998) 112-120.
7. C.S. Iliopoulos, D. Moore, W.F. Smyth, A characterization of the squares in a Fibonacci string, Theoret. Comput. Sci. 172 (1997) 281-291.
8. C.L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York, 1968.
9. F. Mignosi, G. Pirillo, Repetitions in the Fibonacci infinite word, RAIRO Inform. Theor. Appl. 26 (1992) 199-204.
10. P.Séébold, Propriétés combinatoires des mots infinis engendrés par certains morphismes, Report No. 85-16, LITP, Paris, 1985.
11. K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976) 473-482.