Results in Gray Codes and Universal Cycles for Designs

  • Megan Dewar
  • Brett Stevens
Part of the CMS Books in Mathematics book series (CMSBM)


In this chapter we consider Gray codes and universal cycles (Ucycles) for designs. The chapter is broken into three sections: minimal change designs, twofold triple systems, and pairwise balanced designs. In addition to proving the existence of Gray codes and Ucycles for certain designs, we discuss how these results relate to configuration orderings. Cyclic automorphism groups offer a powerful method to construct these orderings by developing in the group to construct partial orderings which can be combined to produce full orderings. This chapter contains the only systematic results that establish the impossibility of some orderings. This chapter is of interest to the researcher wanting to learn about minimal change orderings as opposed to configuration orderings. This chapter is also of interest to a Ucycle researcher interested in seeing construction methods for a different combinatorial family.


Minimal Change Difference Sequence Base Block Triple System Hamilton Cycle 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Megan Dewar
    • 1
  • Brett Stevens
    • 1
  1. 1.School of Mathematics & StatisticsCarleton UniversityOttawaCanada

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