@inproceedings{GregorJaegerMuetze+2018,
Title = {Gray codes and symmetric chains},
Author = {Gregor, Petr and J{\"a}ger, Sven and M{\"u}tze, Torsten and Sawada, Joe and Wille, Kaja},
Booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
Pages = {66:1--66:14},
Year = {2018},
Isbn = {978-3-95977-076-7},
Issn = {1868-8969},
Doi = {10.4230/LIPIcs.ICALP.2018.66},
Location = {Prague},
Address = {Dagstuhl, Germany},
Volume = {107},
Month = {7},
Editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D{\'a}niel and Sannella, Donald},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Abstract = {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. },
Url2 = {http://drops.dagstuhl.de/opus/volltexte/2018/9070/}
}