Combinatorial Gray Code

1. Eades P, McKay B (1984) An algorithm for generating subsets of fixed size with a strong minimal change property. Inf Process Lett 19:131–133

   Article  MathSciNet  MATH  Google Scholar 

2. Ehrlich G (1973) Loopless algorithms for generating permutations, combinations, and other combinatorial configurations. J ACM 20:500–513

   Article  MathSciNet  MATH  Google Scholar 

3. Johnson S (1963) Generation of permutations by adjacent transposition. Math Comput 17:282–285

   Article  MathSciNet  MATH  Google Scholar 

4. Joichi JT, White DE, Williamson SG (1980) Combinatorial Gray codes. SIAM J Comput 9(1):130–141

   Article  MathSciNet  MATH  Google Scholar 

5. Knuth DE (2011) The art of computer programming. Combinatorial algorithms, vol 4A, Part 1. Addison-Wesley, Upper Saddle River, xvi+883pp. ISBN 0-201-03804-8

   Google Scholar 

6. Mütze T (2014) Proof of the middle levels conjecture. arXiv:1404.4442

   Google Scholar 

7. Pruesse G, Ruskey F (1993) Gray codes from antimatroids. Order 10:239–252

   Article  MathSciNet  MATH  Google Scholar 

8. Ruskey F, Sawada J, Williams A (2012) Binary bubble languages. J Comb Theory Ser A 119(1):155–169

   Article  MathSciNet  MATH  Google Scholar 

9. Savage C (1989) Gray code sequences of partitions. J Algorithms 10:577–595

   Article  MathSciNet  MATH  Google Scholar 

10. Savage C (1997) A survey of combinatorial Gray codes. SIAM Rev 39:605–629

    Article  MathSciNet  MATH  Google Scholar 

11. Sawada J, Williams A (2012) Efficient oracles for generating binary bubble languages. Electron J Comb 19:Paper 42

    Google Scholar 

12. Sekanina M (1960) Spisy Přírodovědecké. Fakulty University v Brně 412:137–140

    MathSciNet  Google Scholar 

13. Trotter H (1962) Algorithm 115: Perm. Commun ACM 5:434–435

    Article  Google Scholar 

14. Wilf HS (1989) Combinatorial algorithms: an update. In: CBMS-NSF regional conference series in applied mathematics. SIAM. http://epubs.siam.org/doi/book/10.1137/1.9781611970166

15. Williams A (2013) The greedy Gray code algorithm. In: Algorithms and data structures symposium (WADS 2013), London, Canada. LNCS, vol 8037, pp 525–536

    Google Scholar 

16. Williams A (2014) Hamiltonicity of the Cayley digraph on the symmetric group generated by \(\sigma = (1\ 2\ \cdots \ n)\) and τ = (1 2). arXiv:1307.2549

    Google Scholar 

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