| 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. |
