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	Volume 3, Issue 2 Pg 85 - 164 (April 2009)
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Advances and Applications in Discrete Mathematics

be the set of all n-length binary strings such that there are at least p consecutive 0s between two 1s. Chinburg et al. [3] give a Gray code for the set

such that two consecutive elements differ in at most two positions which are optimal for n large. In this paper, we construct a more restrictive Gray code for

in the sense where our Gray code contains more transitions with one move than theirs. Moreover, using a combinatorial isomorphism between the set of n-length binary strings and the set of n-length permutations avoiding 123 and 132, we provide a bijection from

that induces a Gray code for the set

All these codes can be generated by implementing a recursive algorithm in constant amortized time.

Advances and Applications in Discrete Mathematics
Volume 3, Issue 1, Pages 67 - 84 (January 2009)

GRAY CODE FOR COMPOSITIONS OF n WITH PARTS 1 AND p
Jean-Luc Baril (France) and Céline Moreira Dos Santos (France)

Abstract:
Let

be the set of all n-length binary strings such that there are at least p consecutive 0s between two 1s. Chinburg et al. [3] give a Gray code for the set

such that two consecutive elements differ in at most two positions which are optimal for n large. In this paper, we construct a more restrictive Gray code for