Communications of the ACM
A CAT algorithm for generating permutations with a fixed number of inversions
Information Processing Letters
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
A loop-free two-close Gray-code algorithm for listing k-ary Dyck words
Journal of Discrete Algorithms
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
On Generating the N-ary Reflected Gray Codes
IEEE Transactions on Computers
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Any Gray code for a set of combinatorial objects defines a total order relation on this set: x is less than y if and only if y occurs after x in the Gray code list. Let @? denote the order relation induced by the classical Gray code for the product set (the natural extension of the Binary Reflected Gray Code to k-ary tuples). The restriction of @? to the set of compositions and bounded compositions gives known Gray codes for those sets. Here we show that @? restricted to the set of bounded compositions of an interval yields still a Gray code. An n-composition of an interval is an n-tuple of integers whose sum lies between two integers; and the set of bounded n-compositions of an interval simultaneously generalizes product set and compositions of an integer, and so @? put under a single roof all these Gray codes. As a byproduct we obtain Gray codes for permutations with a number of inversions lying between two integers, and with even/odd number of inversions or cycles. Such particular classes of permutations are used to solve some computational difficult problems.