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Gray codes and symmetric chains
Zitatschlüssel GregorJaegerMuetze+2018
Autor Gregor, Petr and Jäger, Sven and Mütze, Torsten and Sawada, Joe and Wille, Kaja
Buchtitel 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Seiten 66:1–66:14
Jahr 2018
ISBN 978-3-95977-076-7
ISSN 1868-8969
DOI 10.4230/LIPIcs.ICALP.2018.66
Ort Prague
Adresse Dagstuhl, Germany
Jahrgang 107
Monat 7
Herausgeber Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, Dániel and Sannella, Donald
Verlag Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik
Serie Leibniz International Proceedings in Informatics (LIPIcs)
Zusammenfassung 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.
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