Journal of Algorithms
A Gray Code for Necklaces of Fixed Density
SIAM Journal on Discrete Mathematics
An Efficient Algorithm for Generating Necklaces with Fixed Density
SIAM Journal on Computing
Discrete Mathematics
Minimal change list for Lucas strings and some graph theoretic consequences
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Generating gray codes in o(1) worst-case time per word
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Loopless generation of multiset permutations using a constant number of variables by prefix shifts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Gray code for fixed-density necklaces and Lyndon words in constant amortized time
Theoretical Computer Science
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In the last years, the order induced by the Binary Reflected Gray Code or its generalizations shown an increasing interest. In this note we show that the BRGC order induces a cyclic 2-Gray code on the set of binary necklaces and Lyndon words and a cyclic 3-Gray code on the unordered counterparts. This is an improvement and a generalization to unlabeled words of the result in [V. Vajnovszki, Gray code order for Lyndon words, Discrete Math. Theoret. Comput. Sci. 9 (2) (2007) 145-152; M. Weston, V. Vajnovszki, Gray codes for necklaces and Lyndon words of arbitrary base, Pure Mathematics and Applications/Algebra and Theoretical Computer Science, in press]; however an algorithmic implementation of our Gray codes remains an open problem.