Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)

Journal of Algorithms

Volumn 37, Issue 2, 2000, Pages 267-282

  Cattell, Kevin ^a   Ruskey, Frank ^b   Sawada, Joe ^b   Serra, Micaela ^b   Miers, C Robert ^b  

^a HEWLETT PACKARD LABORATORIES   (United States)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003163347     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.2000.1108     Document Type: Article

References (19)

1. J. Berstel and M. Pocchiola, Average cost of Duval's algorithm for generating Lyndon words, Theoret. Comput. Sci. 132 (1994), 415-425.
2. J.-P. Duval, Factoring words over an ordered alphabet, J. Algorithms 4 (1983), 363-381.
3. J.-P. Duval, Génération d'une section des classes de conjugaison et arbre des mots de Lyndon de longueur bornée, Theoret. Comput. Sci. 60 (1988), 255-283.
4. M. C. Er, A fast algorithm for generating set partitions, Comput. J. 31 (1988), 283-284.
5. H. Fredricksen and I. J. Kessler, An algorithm for generating necklaces of beads in two colors, Discrete Math. 61 (1986), 181-188.
6. H. Fredricksen and I. J. Maiorana, Necklaces of beads in k colors and k-ary de Bruijn sequences, Discrete Math. 23 (1978), 207-210.
7. 2," Technical report tr-rsfb-96-018, University of Paderborn, Germany, 1996.
8. E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math. 5 (1961), 657-665.
9. S. W. Golomb, "Irreducible Polynomials, Synchronization Codes, Primitive Necklaces, and the Cyclotomic Algebra," Univ. of North Carolina Monograph Series in Probability and Statistics, Vol. 4, pp. 358-370, 1967.
10. S. W. Golomb, "Shift Register Sequences," Holden-Day, Oakland, 1967.
11. R. L. Graham, D. E. Knuth, and O. Patashnik, "Concrete Mathematics," Addison-Wesley, Reading, MA, 1989.
12. R. A. Kaye, A Gray code for set partitions, Inform. Process. Lett. 5 (1976), 171-173.
13. D. E. Knuth, "Axioms and Hulls," Lecture Notes in Compu ter Science, Vol. 606, Springer-Verlag, Berlin/New York, 1992.
14. R. Lidl and H. Niederreiter, "Introduction to Finite Fields and Their Applications," Cambridge Univ. Press, Cambridge, UK, 1994.
15. H. Lüneburg, "Tools and Fundamental Constructions of Combinatorial Mathematics," Wissenschafts, 1989.
16. M. Lothaire, "Combinatorics on Words," Cambridge Univ. Press, Cambridge, UK, 1983.
17. A. Proskurowski, F. Ruskey, and M. Smith, Analysis of algorithms for listing equivalence classes of k-ary strings induced by simple group actions, SIAM J. Discrete Math. 11 (1998), 94-109.
18. C. Reutenauer, "Free Lie Algebras," Clarendon Press, Oxford, 1993.
19. F. Ruskev, Combinatorial generation, manuscript, course notes for CSC 528, Univ. Journal of Algorithms 37, 451-467 (2000)