Abstract
We present three related results about simple combinatorial Gray codes constructed recursively by reversing certain sublists. First, we show a bijection between the list of compositions of Knuth and the list of combinations of Eades and McKay. Secondly, we provide a short description of a list of combinations satisfying a more restrictive closeness criteria of Chase. Finally, we develop a new, simply described, Gray code list of the partitions of a set into a fixed number of blocks, as represented by restricted growth sequences. In each case the recursive definition of the list is easily translatable into an algorithm for generating the list in time proportional to the number of elements in the list; i.e., each object is produced in O(1) amortized time by the algorithm.
Research supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A3379.
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© 1993 Springer-Verlag Berlin Heidelberg
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Ruskey, F. (1993). Simple combinatorial Gray codes constructed by reversing sublists. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_250
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DOI: https://doi.org/10.1007/3-540-57568-5_250
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