Issue
RAIRO-Theor. Inf. Appl.
Volume 59, 2025
Generation, enumeration and tiling
Article Number 21
Number of page(s) 14
DOI https://doi.org/10.1051/ita/2025019
Published online 03 December 2025
  1. F. Ruskey and A. Williams, An explicit universal cycle for the (n-l)-permutations of an n-set. ACM Trans. Algorithms 6 (2010) 1-12. [Google Scholar]
  2. D.E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd edn., vol. 2. Addison-Wesley, Reading, MA (1997). [Google Scholar]
  3. J.G. Propp and D.B. Wilson, How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph. J. Algorithms 27 (1998) 170-217. [Google Scholar]
  4. D. Gabric and J. Sawada, Constructing de Bruijn sequences by concatenating smaller universal cycles. Theoret. Comput. Sci. 743 (2018) 12-22. [Google Scholar]
  5. F. Ruskey, J. Sawada and A. Williams, De Bruijn sequences for fixed-weight binary strings. SIAM J. Discrete Math. 26 (2012) 605-617. [Google Scholar]
  6. S.F. Altschul and B.W. Erickson, Significance of nucleotide sequence alignments: a method for random sequence permutation that preserves dinucleotide and codon usage. Mol. Biol. Evol. 2 (1985) 526-538. [Google Scholar]
  7. Z.-D. Dai, K. Martin, B. Robshaw and P. Wild, Orientable sequences, in Cryptography and Coding III, edited by M.J. Ganley. Oxford University Press (1993) 97-115. [Google Scholar]
  8. P.-H. Fleury, Deux problemes de geometrie de situation. J. Math. element. 42 (1883) 257-261. [Google Scholar]
  9. Z. Liptak and L. Parmigiani, A BWT-based algorithm for random de Bruijn sequence construction, in LATIN 2024. LNCS 14578 (2024) 130-145. [Google Scholar]
  10. R.A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research. Oliver and Boyd, London (1938). [Google Scholar]
  11. J. Arndt, Generating Random Permutations. Phd thesis, Australian National University (2010). [Google Scholar]
  12. D. Kandel, Y. Matias, R. Unger and P. Winkler, Shuffling biological sequences. Discrete Appl. Math. 71 (1996) 171-185. [Google Scholar]
  13. J. Sawada and A. Williams, A universal cycle for strings with fixed-content. Algorithmica 85 (2023) 1754-1785. [Google Scholar]
  14. A.E. Holroyd, F. Ruskey and A. Williams, Shorthand universal cycles for permutations. Algorithmica 64 (2012) 215-245. [Google Scholar]
  15. J. Sawada, A. Williams and D. Wong, Generalizing the classic greedy and necklace constructions of de Bruijn sequences and universal cycles. Electron. J. Combin. 23 (2016) Paper 1.24, 20. [Google Scholar]
  16. J. Sawada, J. Sears, A. Trautrim and A. Williams, Concatenation trees: a framework for efficient universal cycle and de Bruijn sequence constructions. arXiv preprint arXiv:2308.12405 (2024). [Google Scholar]
  17. J. Sawada and D. Wong, Efficient universal cycle constructions for weak orders. Discrete Math. 343 (2020) 112022. [Google Scholar]
  18. OEIS Foundation Inc. Entry A000670 in The On-Line Encyclopedia of Integer Sequences (2025). https://oeis.org/{A}000670. [Google Scholar]
  19. De Bruijn sequence and universal cycle constructions (2025). http://debruijnsequence.org. [Google Scholar]
  20. Y. M. Chee, T. Etzion, T.L. Nguyen, D.H. Ta, V.D. Tran and V.K. Vu, Maximum length RLL sequences in de Bruijn graph, arXiv preprint arXiv:2403.01454 (2024). [Google Scholar]
  21. D.B. Wilson Generating random spanning trees more quickly than the cover time, in Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing (New York, NY, USA), STOC '96 (Association for Computing Machinery) (1996) 296-303. [Google Scholar]
  22. D. Gabrić and J. Sawada, Constructing k-ary orientable sequences with asymptotically optimal length. Designs, Codes and Cryptography (2025). [Google Scholar]
  23. A. Alhakim, C.J. Mitchell, J. Szmidt and P.R. Wild, Orientable sequences over non-binary alphabets, in Cryptography and Communications 16 (2024) 1309-1326. [Google Scholar]
  24. J. Burns and C. Mitchell, Position sensing coding schemes, in Cryptography and Coding III, edited by M.J. Ganley. Oxford University Press (1993) 31-66. [Google Scholar]
  25. R. Durstenfeld, Algorithm 235: random permutation. Commun. ACM 7 (1964) 420. [Google Scholar]
  26. D. Gabric, J. Sawada, A. Williams and D. Wong, A successor rule framework for constructing k-ary de Bruijn sequences and universal cycles. IEEE Trans. Inform. Theory 66 (2020) 679-687. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.