Gregor, Petr
[Author];
Jäger, Sven
[Author];
Mütze, Torsten
[Author];
Sawada, Joe
[Author];
Wille, Kaja
[Author]
;
Petr Gregor and Sven Jäger and Torsten Mütze and Joe Sawada and Kaja Wille
[Contributor]
Footnote:
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Description:
We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1-l,n+l], where 1 <= l <= n+1, by flipping a single bit in each step. This is a far-ranging generalization of the well-known middle two levels problem (l=1). We provide a solution for the case l=2 and solve a relaxed version of the problem for general values of l, by constructing cycle factors for those instances. Our proof uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets, and we present several new constructions of such decompositions. In particular, we construct four pairwise edge-disjoint symmetric chain decompositions of the n-dimensional hypercube for any n >= 12.